diff --git a/admin/tool/dataprivacy/classes/external.php b/admin/tool/dataprivacy/classes/external.php
index 15cfc191617..6938126c590 100644
--- a/admin/tool/dataprivacy/classes/external.php
+++ b/admin/tool/dataprivacy/classes/external.php
@@ -708,7 +708,7 @@ class external extends external_api {
             $fields .= ',' . implode(',', $extrafields);
         }
 
-        list($sql, $params) = users_search_sql($query, '', false, $extrafields, $excludedusers);
+        list($sql, $params) = users_search_sql($query, '', USER_SEARCH_STARTS_WITH, $extrafields, $excludedusers);
         $users = $DB->get_records_select('user', $sql, $params, $sort, $fields, 0, 30);
         $useroptions = [];
         foreach ($users as $user) {
diff --git a/admin/tool/lp/classes/external.php b/admin/tool/lp/classes/external.php
index 4d7990ca50c..f5585d19ee2 100644
--- a/admin/tool/lp/classes/external.php
+++ b/admin/tool/lp/classes/external.php
@@ -874,7 +874,7 @@ class external extends external_api {
         $fields = $userfieldsapi->get_sql('u', false, '', '', false)->selects;
         $extrasearchfields = $userfieldsapi->get_required_fields([\core_user\fields::PURPOSE_IDENTITY]);
 
-        list($wheresql, $whereparams) = users_search_sql($query, 'u', true, $extrasearchfields);
+        list($wheresql, $whereparams) = users_search_sql($query, 'u', USER_SEARCH_CONTAINS, $extrasearchfields);
         list($sortsql, $sortparams) = users_order_by_sql('u', $query, $context);
 
         $countsql = "SELECT COUNT('x') FROM {user} u WHERE $wheresql AND u.id $filtercapsql";
diff --git a/enrol/ajax.php b/enrol/ajax.php
index fab67db13f2..c128b003b74 100644
--- a/enrol/ajax.php
+++ b/enrol/ajax.php
@@ -58,7 +58,7 @@ $outcome->success = true;
 $outcome->response = new stdClass();
 $outcome->error = '';
 
-$searchanywhere = get_user_preferences('userselector_searchanywhere', false);
+$searchanywhere = get_user_preferences('userselector_searchtype') === USER_SEARCH_CONTAINS ? true : false;
 
 switch ($action) {
     case 'unenrol':
diff --git a/enrol/locallib.php b/enrol/locallib.php
index beeb013e72d..b706ad230ba 100644
--- a/enrol/locallib.php
+++ b/enrol/locallib.php
@@ -274,7 +274,7 @@ class course_enrolment_manager {
         // Search condition.
         // TODO Does not support custom user profile fields (MDL-70456).
         $extrafields = fields::get_identity_fields($this->get_context(), false);
-        list($sql, $params) = users_search_sql($this->searchfilter, 'u', true, $extrafields);
+        list($sql, $params) = users_search_sql($this->searchfilter, 'u', USER_SEARCH_CONTAINS, $extrafields);
 
         // Role condition.
         if ($this->rolefilter) {
diff --git a/enrol/manual/ajax.php b/enrol/manual/ajax.php
index 22ccef20ebb..8a358a552f0 100644
--- a/enrol/manual/ajax.php
+++ b/enrol/manual/ajax.php
@@ -60,7 +60,7 @@ $outcome->response = new stdClass();
 $outcome->error = '';
 $outcome->count = 0;
 
-$searchanywhere = get_user_preferences('userselector_searchanywhere', false);
+$searchanywhere = get_user_preferences('userselector_searchtype') === USER_SEARCH_CONTAINS ? true : false;
 
 switch ($action) {
     case 'enrol':
diff --git a/grade/report/history/classes/helper.php b/grade/report/history/classes/helper.php
index 189cbf7b022..c4d8b1ba8e6 100644
--- a/grade/report/history/classes/helper.php
+++ b/grade/report/history/classes/helper.php
@@ -138,7 +138,7 @@ class helper {
         }
         $params = array();
         if (!empty($search)) {
-            list($filtersql, $params) = users_search_sql($search, 'u', true, $extrafields);
+            list($filtersql, $params) = users_search_sql($search, 'u', USER_SEARCH_CONTAINS, $extrafields);
             $filtersql .= ' AND ';
         } else {
             $filtersql = '';
diff --git a/lang/en/moodle.php b/lang/en/moodle.php
index 5dca5a85c8d..2fe0a1d9d27 100644
--- a/lang/en/moodle.php
+++ b/lang/en/moodle.php
@@ -2357,7 +2357,10 @@ $string['userpic'] = 'User picture';
 $string['users'] = 'Users';
 $string['userselectorautoselectunique'] = 'If only one user matches the search, select them automatically';
 $string['userselectorpreserveselected'] = 'Keep selected users, even if they no longer match the search';
-$string['userselectorsearchanywhere'] = 'Match the search text anywhere in the displayed fields';
+$string['userselectorsearchmatching'] = 'Matching:';
+$string['userselectorsearchfromstart'] = 'from start';
+$string['userselectorsearchanywhere'] = 'anywhere';
+$string['userselectorsearchexactmatchonly'] = 'exact matches only';
 $string['usersnew'] = 'New users';
 $string['usersnoaccesssince'] = 'Inactive for more than';
 $string['userpreferences'] = 'User preferences';
diff --git a/lib/classes/user.php b/lib/classes/user.php
index 7fa691bb1a2..6641c26acdc 100644
--- a/lib/classes/user.php
+++ b/lib/classes/user.php
@@ -243,7 +243,7 @@ class core_user {
         }
 
         // Start building the WHERE clause based on name.
-        list ($where, $whereparams) = users_search_sql($query, 'u', false);
+        list ($where, $whereparams) = users_search_sql($query, 'u');
 
         // We allow users to search with extra identity fields (as well as name) but only if they
         // have the permission to display those identity fields.
@@ -1021,10 +1021,10 @@ class core_user {
             'default' => false,
             'permissioncallback' => [static::class, 'is_current_user'],
         ];
-        $preferences['userselector_searchanywhere'] = [
-            'type' => PARAM_BOOL,
+        $preferences['userselector_searchtype'] = [
+            'type' => PARAM_INT,
             'null' => NULL_NOT_ALLOWED,
-            'default' => false,
+            'default' => USER_SEARCH_STARTS_WITH,
             'permissioncallback' => [static::class, 'is_current_user'],
         ];
         $preferences['question_bank_advanced_search'] = [
diff --git a/lib/datalib.php b/lib/datalib.php
index 20a2f66f0f6..2dbaae9cf9a 100644
--- a/lib/datalib.php
+++ b/lib/datalib.php
@@ -52,6 +52,12 @@ define('MAX_COURSE_CATEGORIES', 10000);
 if (!defined('LASTACCESS_UPDATE_SECS')) {
     define('LASTACCESS_UPDATE_SECS', 60);
 }
+/**
+ * The constant value when we use the search option.
+ */
+define('USER_SEARCH_STARTS_WITH', 0);
+define('USER_SEARCH_CONTAINS', 1);
+define('USER_SEARCH_EXACT_MATCH', 2);
 
 /**
  * Returns $user object of the main admin user
@@ -216,8 +222,8 @@ function search_users($courseid, $groupid, $searchtext, $sort='', array $excepti
  * @param string $search the text to search for (empty string = find all)
  * @param string $u the table alias for the user table in the query being
  *     built. May be ''.
- * @param bool $searchanywhere If true (default), searches in the middle of
- *     names, otherwise only searches at start
+ * @param int $searchtype If 0(default): searches at start, 1: searches in the middle of names
+ *      2: search exact match.
  * @param array $extrafields Array of extra user fields to include in search, must be prefixed with table alias if they are not in
  *     the user table.
  * @param array $exclude Array of user ids to exclude (empty = don't exclude)
@@ -227,7 +233,7 @@ function search_users($courseid, $groupid, $searchtext, $sort='', array $excepti
  *     where clause the query, and an associative array containing any required
  *     parameters (using named placeholders).
  */
-function users_search_sql(string $search, string $u = 'u', bool $searchanywhere = true, array $extrafields = [],
+function users_search_sql(string $search, string $u = 'u', int $searchtype = USER_SEARCH_STARTS_WITH, array $extrafields = [],
         array $exclude = null, array $includeonly = null): array {
     global $DB, $CFG;
     $params = array();
@@ -237,7 +243,6 @@ function users_search_sql(string $search, string $u = 'u', bool $searchanywhere
         $u .= '.';
     }
 
-    // If we have a $search string, put a field LIKE '$search%' condition on each field.
     if ($search) {
         $conditions = array(
             $DB->sql_fullname($u . 'firstname', $u . 'lastname'),
@@ -247,14 +252,26 @@ function users_search_sql(string $search, string $u = 'u', bool $searchanywhere
             // Add the table alias for the user table if the field doesn't already have an alias.
             $conditions[] = strpos($field, '.') !== false ? $field : $u . $field;
         }
-        if ($searchanywhere) {
-            $searchparam = '%' . $search . '%';
-        } else {
-            $searchparam = $search . '%';
+        switch ($searchtype) {
+            case USER_SEARCH_STARTS_WITH:
+                // Put a field LIKE 'search%' condition on each field.
+                $searchparam = $search . '%';
+                break;
+            case USER_SEARCH_CONTAINS:
+                // Put a field LIKE '$search%' condition on each field.
+                $searchparam = '%' . $search . '%';
+                break;
+            case USER_SEARCH_EXACT_MATCH:
+                // Match exact the $search string.
+                $searchparam = $search;
+                break;
         }
         $i = 0;
         foreach ($conditions as $key => $condition) {
             $conditions[$key] = $DB->sql_like($condition, ":con{$i}00", false, false);
+            if ($searchtype === USER_SEARCH_EXACT_MATCH) {
+                $conditions[$key] = "$condition = :con{$i}00";
+            }
             $params["con{$i}00"] = $searchparam;
             $i++;
         }
diff --git a/lib/db/upgrade.php b/lib/db/upgrade.php
index d7c933474a9..b84be3be63c 100644
--- a/lib/db/upgrade.php
+++ b/lib/db/upgrade.php
@@ -3594,5 +3594,12 @@ privatefiles,moodle|/user/files.php';
         upgrade_main_savepoint(true, 2023090200.01);
     }
 
+    if ($oldversion < 2023090800.00) {
+        // Delete all the searchanywhere prefs in user_preferences table.
+        $DB->delete_records('user_preferences', ['name' => 'userselector_searchanywhere']);
+        // Main savepoint reached.
+        upgrade_main_savepoint(true, 2023090800.00);
+    }
+
     return true;
 }
diff --git a/lib/tests/datalib_test.php b/lib/tests/datalib_test.php
index 9f36dd925f1..134176da19c 100644
--- a/lib/tests/datalib_test.php
+++ b/lib/tests/datalib_test.php
@@ -77,42 +77,48 @@ class datalib_test extends \advanced_testcase {
         $user2 = self::getDataGenerator()->create_user($user2);
 
         // Search by name (anywhere in text).
-        list($sql, $params) = users_search_sql('User Test 2', '');
+        list($sql, $params) = users_search_sql('User Test 2', '', USER_SEARCH_CONTAINS);
         $results = $DB->get_records_sql("SELECT id FROM {user} WHERE $sql ORDER BY username", $params);
         $this->assertFalse(array_key_exists($user1->id, $results));
         $this->assertTrue(array_key_exists($user2->id, $results));
 
         // Search by (most of) full name.
-        list($sql, $params) = users_search_sql('First Name User Test 2 Last Name User', '');
+        list($sql, $params) = users_search_sql('First Name User Test 2 Last Name User', '', USER_SEARCH_CONTAINS);
         $results = $DB->get_records_sql("SELECT id FROM {user} WHERE $sql ORDER BY username", $params);
         $this->assertFalse(array_key_exists($user1->id, $results));
         $this->assertTrue(array_key_exists($user2->id, $results));
 
         // Search by name (start of text) valid or not.
-        list($sql, $params) = users_search_sql('User Test 2', '', false);
+        list($sql, $params) = users_search_sql('User Test 2', '');
         $results = $DB->get_records_sql("SELECT id FROM {user} WHERE $sql ORDER BY username", $params);
         $this->assertEquals(0, count($results));
-        list($sql, $params) = users_search_sql('First Name User Test 2', '', false);
+        list($sql, $params) = users_search_sql('First Name User Test 2', '');
         $results = $DB->get_records_sql("SELECT id FROM {user} WHERE $sql ORDER BY username", $params);
         $this->assertFalse(array_key_exists($user1->id, $results));
         $this->assertTrue(array_key_exists($user2->id, $results));
 
         // Search by extra fields included or not (address).
-        list($sql, $params) = users_search_sql('Test Street', '', true);
+        list($sql, $params) = users_search_sql('Test Street', '', USER_SEARCH_CONTAINS);
         $results = $DB->get_records_sql("SELECT id FROM {user} WHERE $sql ORDER BY username", $params);
         $this->assertCount(0, $results);
-        list($sql, $params) = users_search_sql('Test Street', '', true, array('address'));
+        list($sql, $params) = users_search_sql('Test Street', '', USER_SEARCH_CONTAINS, array('address'));
         $results = $DB->get_records_sql("SELECT id FROM {user} WHERE $sql ORDER BY username", $params);
         $this->assertCount(2, $results);
 
         // Exclude user.
-        list($sql, $params) = users_search_sql('User Test', '', true, array(), array($user1->id));
+        list($sql, $params) = users_search_sql('User Test', '', USER_SEARCH_CONTAINS, array(), array($user1->id));
         $results = $DB->get_records_sql("SELECT id FROM {user} WHERE $sql ORDER BY username", $params);
         $this->assertFalse(array_key_exists($user1->id, $results));
         $this->assertTrue(array_key_exists($user2->id, $results));
 
         // Include only user.
-        list($sql, $params) = users_search_sql('User Test', '', true, array(), array(), array($user1->id));
+        list($sql, $params) = users_search_sql('User Test', '', USER_SEARCH_CONTAINS, array(), array(), array($user1->id));
+        $results = $DB->get_records_sql("SELECT id FROM {user} WHERE $sql ORDER BY username", $params);
+        $this->assertTrue(array_key_exists($user1->id, $results));
+        $this->assertFalse(array_key_exists($user2->id, $results));
+
+        // Exact match only.
+        [$sql, $params] = users_search_sql('Last Name User Test 1', '', USER_SEARCH_EXACT_MATCH, [], null, null, true);
         $results = $DB->get_records_sql("SELECT id FROM {user} WHERE $sql ORDER BY username", $params);
         $this->assertTrue(array_key_exists($user1->id, $results));
         $this->assertFalse(array_key_exists($user2->id, $results));
@@ -120,7 +126,7 @@ class datalib_test extends \advanced_testcase {
         // Join with another table and use different prefix.
         set_user_preference('amphibian', 'frog', $user1);
         set_user_preference('amphibian', 'salamander', $user2);
-        list($sql, $params) = users_search_sql('User Test 1', 'qq');
+        list($sql, $params) = users_search_sql('User Test 1', 'qq', USER_SEARCH_CONTAINS);
         $results = $DB->get_records_sql("
                 SELECT up.id, up.value
                   FROM {user} qq
@@ -135,7 +141,7 @@ class datalib_test extends \advanced_testcase {
         // Join with another table and include other table fields in search.
         set_user_preference('reptile', 'snake', $user1);
         set_user_preference('reptile', 'lizard', $user2);
-        list($sql, $params) = users_search_sql('snake', 'qq', true, ['up.value']);
+        list($sql, $params) = users_search_sql('snake', 'qq', USER_SEARCH_CONTAINS, ['up.value']);
         $results = $DB->get_records_sql("
                 SELECT up.id, up.value
                   FROM {user} qq
diff --git a/lib/upgrade.txt b/lib/upgrade.txt
index 96daf7fce74..f0f1ac656a6 100644
--- a/lib/upgrade.txt
+++ b/lib/upgrade.txt
@@ -169,6 +169,9 @@ being forced open in all behat tests.
 * Added a new method called exceeds_password_length in moodlelib.php to validate the password length.
 * The core/modal_factory has been deprecated. From Moodle 4.3 onwards please instantiate new modals using the ModalType.create method instead.
   Please note that this method does not support the `trigger` option.
+* The users_search_sql function parameter $searchanywhere has been change to $searchtype for different type of search. $searchtype is a int parameter and has three constant value:
+  USER_SEARCH_STARTS_WITH: 0, USER_SEARCH_CONTAINS: 1, USER_SEARCH_EXACT_MATCH: 2
+  See MDL-78312 for further information.
 
 === 4.2 ===
 
diff --git a/user/classes/external/search_identity.php b/user/classes/external/search_identity.php
index e4419ee0a8f..45b9e4a65d6 100644
--- a/user/classes/external/search_identity.php
+++ b/user/classes/external/search_identity.php
@@ -68,7 +68,7 @@ class search_identity extends external_api {
         $fields = \core_user\fields::for_name()->with_identity($context, false);
         $extrafields = $fields->get_required_fields([\core_user\fields::PURPOSE_IDENTITY]);
 
-        list($searchsql, $searchparams) = users_search_sql($query, '', true, $extrafields);
+        list($searchsql, $searchparams) = users_search_sql($query, '', USER_SEARCH_CONTAINS, $extrafields);
         list($sortsql, $sortparams) = users_order_by_sql('', $query, $context);
         $params = array_merge($searchparams, $sortparams);
 
diff --git a/user/selector/lib.php b/user/selector/lib.php
index 1b79cec5056..d69d30a6473 100644
--- a/user/selector/lib.php
+++ b/user/selector/lib.php
@@ -58,9 +58,9 @@ abstract class user_selector_base {
     protected $preserveselected = false;
     /** @var boolean If only one user matches the search, should we select them automatically. */
     protected $autoselectunique = false;
-    /** @var boolean When searching, do we only match the starts of fields (better performance)
-     * or do we match occurrences anywhere? */
-    protected $searchanywhere = false;
+    /** @var int When searching, do we only match the starts of fields (better performance)
+     * or do we match occurrences anywhere or do we match exact the fields. */
+    protected $searchtype = USER_SEARCH_STARTS_WITH;
     /** @var mixed This is used by get selected users */
     protected $validatinguserids = null;
 
@@ -156,8 +156,7 @@ abstract class user_selector_base {
         // Read the user prefs / optional_params that we use.
         $this->preserveselected = $this->initialise_option('userselector_preserveselected', $this->preserveselected);
         $this->autoselectunique = $this->initialise_option('userselector_autoselectunique', $this->autoselectunique);
-        $this->searchanywhere = $this->initialise_option('userselector_searchanywhere', $this->searchanywhere);
-
+        $this->searchtype = (int) $this->initialise_option('userselector_searchtype', $this->searchtype, PARAM_INT);
         if (!empty($CFG->maxusersperpage)) {
             $this->maxusersperpage = $CFG->maxusersperpage;
         }
@@ -278,7 +277,6 @@ abstract class user_selector_base {
                 $this->name . '_clearbutton" value="' . get_string('clear') . '" class="btn btn-secondary"/>';
 
         // And the search options.
-        $optionsoutput = false;
         if (!user_selector_base::$searchoptionsoutput) {
             $output .= print_collapsible_region_start('', 'userselector_options',
                 get_string('searchoptions'), 'userselector_optionscollapsed', true, true);
@@ -286,8 +284,7 @@ abstract class user_selector_base {
                 get_string('userselectorpreserveselected'));
             $output .= $this->option_checkbox('autoselectunique', $this->autoselectunique,
                 get_string('userselectorautoselectunique'));
-            $output .= $this->option_checkbox('searchanywhere', $this->searchanywhere,
-                get_string('userselectorsearchanywhere'));
+            $output .= $this->output_searchtype_radios();
             $output .= print_collapsible_region_end(true);
 
             $PAGE->requires->js_init_call('M.core_user.init_user_selector_options_tracker', array(), false, self::$jsmodule);
@@ -499,8 +496,7 @@ abstract class user_selector_base {
         $extrafields = $this->includecustomfields
             ? array_values($this->userfieldsmappings)
             : $this->extrafields;
-
-        return users_search_sql($search, $u, $this->searchanywhere, $extrafields,
+        return users_search_sql($search, $u, $this->searchtype, $extrafields,
                 $this->exclude, $this->validatinguserids);
     }
 
@@ -644,10 +640,11 @@ abstract class user_selector_base {
      *
      * @param string $name
      * @param mixed $default
+     * @param string $paramtype allow the option to custom param type. default is bool
      * @return mixed|null|string
      */
-    private function initialise_option($name, $default) {
-        $param = optional_param($name, null, PARAM_BOOL);
+    private function initialise_option($name, $default, $paramtype = PARAM_BOOL) {
+        $param = optional_param($name, null, $paramtype);
         if (is_null($param)) {
             return get_user_preferences($name, $default);
         } else {
@@ -673,7 +670,7 @@ abstract class user_selector_base {
         $name = 'userselector_' . $name;
         // For the benefit of brain-dead IE, the id must be different from the name of the hidden form field above.
         // It seems that document.getElementById('frog') in IE will return and element with name="frog".
-        $output = '<div class="form-check"><input type="hidden" name="' . $name . '" value="0" />' .
+        $output = '<div class="form-check justify-content-start ml-1"><input type="hidden" name="' . $name . '" value="0" />' .
                     '<label class="form-check-label" for="' . $name . 'id">' .
                         '<input class="form-check-input" type="checkbox" id="' . $name . 'id" name="' . $name .
                             '" value="1"' . $checked . ' /> ' . $label .
@@ -682,6 +679,48 @@ abstract class user_selector_base {
         return $output;
     }
 
+    /**
+     * Get all the data for each input in the user selector search type.
+     *
+     * @param string $name
+     * @param bool $checked
+     * @param string $label
+     * @param int $value
+     * @param string $class
+     * @return array a list of attributes for input.
+     */
+    private function get_radio_searchtype_data(string $name, bool $checked, string $label, int $value, string $class): array {
+        $name = 'userselector_' . $name;
+        $id = $name . 'id';
+        $attrs = [
+            'value' => $value,
+            'id' => $id,
+            'name' => $name,
+            'class' => $class,
+            'label' => $label,
+        ];
+        if ($checked) {
+            $attrs['checked'] = true;
+        }
+        return $attrs;
+    }
+
+    /**
+     * Output the search type radio buttons.
+     *
+     * @return string
+     */
+    private function output_searchtype_radios(): string {
+        global $OUTPUT;
+        $fields[] = $this->get_radio_searchtype_data('searchexactmatchesonly', $this->searchtype === USER_SEARCH_EXACT_MATCH,
+            get_string('userselectorsearchexactmatchonly'), USER_SEARCH_EXACT_MATCH, 'mr-1');
+        $fields[] = $this->get_radio_searchtype_data('searchfromstart', $this->searchtype === USER_SEARCH_STARTS_WITH,
+            get_string('userselectorsearchfromstart'), USER_SEARCH_STARTS_WITH, 'mr-1');
+        $fields[] = $this->get_radio_searchtype_data('searchanywhere', $this->searchtype === USER_SEARCH_CONTAINS,
+            get_string('userselectorsearchanywhere'), USER_SEARCH_CONTAINS, 'mr-1');
+        return $OUTPUT->render_from_template('core_user/form_user_selector_searchtype', (object) ['fields' => $fields]);
+    }
+
     /**
      * Initialises JS for this control.
      *
@@ -689,7 +728,7 @@ abstract class user_selector_base {
      * @return string any HTML needed here.
      */
     protected function initialise_javascript($search) {
-        global $USER, $PAGE, $OUTPUT;
+        global $USER, $PAGE;
         $output = '';
 
         // Put the options into the session, to allow search.php to respond to the ajax requests.
@@ -700,7 +739,7 @@ abstract class user_selector_base {
         // Initialise the selector.
         $PAGE->requires->js_init_call(
             'M.core_user.init_user_selector',
-            array($this->name, $hash, $this->extrafields, $search),
+            array($this->name, $hash, $this->extrafields, $search, $this->searchtype),
             false,
             self::$jsmodule
         );
diff --git a/user/selector/module.js b/user/selector/module.js
index 1eed6fa8322..331ceecc503 100644
--- a/user/selector/module.js
+++ b/user/selector/module.js
@@ -25,8 +25,9 @@ M.core_user.get_user_selector = function (name) {
  * @param {string} hash the hash that identifies this selector in the user's session.
  * @param {array} extrafields extra fields we are displaying for each user in addition to fullname.
  * @param {string} lastsearch The last search that took place
+ * @param {int} searchtype the last search option that took place
  */
-M.core_user.init_user_selector = function (Y, name, hash, extrafields, lastsearch) {
+M.core_user.init_user_selector = function(Y, name, hash, extrafields, lastsearch, searchtype) {
     // Creates a new user_selector object
     var user_selector = {
         /** This id/name used for this control in the HTML. */
@@ -50,6 +51,8 @@ M.core_user.init_user_selector = function (Y, name, hash, extrafields, lastsearc
         /** Whether any options where selected last time we checked. Used by
          *  handle_selection_change to track when this status changes. */
         selectionempty : true,
+        /** The last search option that we use for*/
+        searchtype: searchtype,
         /**
          * Initialises the user selector object
          * @constructor
@@ -69,7 +72,9 @@ M.core_user.init_user_selector = function (Y, name, hash, extrafields, lastsearc
             this.listbox.on('change', this.handle_selection_change, this);
 
             // And when the search any substring preference changes. Do an immediate re-search.
-            Y.one('#userselector_searchanywhereid').on('click', this.handle_searchanywhere_change, this);
+            Y.one('#userselector_searchfromstartid').on('click', this.handle_searchtype_change, this);
+            Y.one('#userselector_searchanywhereid').on('click', this.handle_searchtype_change, this);
+            Y.one('#userselector_searchexactmatchesonlyid').on('click', this.handle_searchtype_change, this);
 
             // Define our custom event.
             //this.createEvent('selectionchanged');
@@ -114,13 +119,22 @@ M.core_user.init_user_selector = function (Y, name, hash, extrafields, lastsearc
             this.selectionempty = isselectionempty;
         },
         /**
-         * Trigger a re-search when the 'search any substring' option is changed.
+         * Trigger a re-search and set the user prefs when the search radio option is changed.
+         *
+         *  @param {Y.Event} e the change event.
          */
-        handle_searchanywhere_change : function() {
+        handle_searchtype_change: function(e) {
+            this.clear_search_radio_state();
+            e.currentTarget.set('checked', 1);
+            this.searchtype = e.currentTarget.get('value');
+            require(['core_user/repository'], function(UserRepository) {
+                UserRepository.setUserPreference('userselector_searchtype', e.currentTarget.get('value'));
+            });
             if (this.lastsearch != '' && this.get_search_text() != '') {
                 this.send_query(true);
             }
         },
+
         /**
          * Click handler for the clear button..
          */
@@ -129,6 +143,16 @@ M.core_user.init_user_selector = function (Y, name, hash, extrafields, lastsearc
             this.clearbutton.set('disabled',true);
             this.send_query(false);
         },
+
+        /**
+         * Clear all checked state in the radio search option.
+         */
+        clear_search_radio_state: function() {
+            Y.one('#userselector_searchfromstartid').set('checked', 0);
+            Y.one('#userselector_searchanywhereid').set('checked', 0);
+            Y.one('#userselector_searchexactmatchesonlyid').set('checked', 0);
+        },
+
         /**
          * Fires off the ajax search request.
          */
@@ -146,10 +170,10 @@ M.core_user.init_user_selector = function (Y, name, hash, extrafields, lastsearc
             Y.Object.each(this.iotransactions, function(trans) {
                 trans.abort();
             });
-
             var iotrans = Y.io(M.cfg.wwwroot + '/user/selector/search.php', {
                 method: 'POST',
-                data: 'selectorid=' + hash + '&sesskey=' + M.cfg.sesskey + '&search=' + value + '&userselector_searchanywhere=' + this.get_option('searchanywhere'),
+                data: 'selectorid=' + hash + '&sesskey=' + M.cfg.sesskey +
+                    '&search=' + value + '&userselector_searchtype=' + this.searchtype,
                 on: {
                     complete: this.handle_response
                 },
@@ -355,7 +379,6 @@ M.core_user.init_user_selector_options_tracker = function(Y) {
             var settings = [
                 'userselector_preserveselected',
                 'userselector_autoselectunique',
-                'userselector_searchanywhere'
             ];
             for (var s in settings) {
                 var setting = settings[s];
diff --git a/user/templates/form_user_selector_searchtype.mustache b/user/templates/form_user_selector_searchtype.mustache
new file mode 100644
index 00000000000..09d16192ba0
--- /dev/null
+++ b/user/templates/form_user_selector_searchtype.mustache
@@ -0,0 +1,47 @@
+{{!
+    This file is part of Moodle - http://moodle.org/
+
+    Moodle is free software: you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    Moodle is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with Moodle.  If not, see <http://www.gnu.org/licenses/>.
+}}
+{{!
+    @template core_user/form_user_selector_searchtype
+
+    Template for the form_user_selector search type.
+
+    Context variables required for this template:
+    * defaultvalue int - The user's full name.
+    * fields list - the input element attributes and label
+
+    Example context (json):
+       {
+           "fields": [
+               {
+                   "id": "id",
+                   "name": "userselector_searchexactmatchesonly",
+                   "class": "class",
+                   "label": "Search anywhere",
+                   "checked": true
+               }
+           ]
+       }
+}}
+<div class="form-check justify-content-start ml-1">
+   <span class="mr-1">{{#str}}userselectorsearchmatching, core{{/str}}</span>
+{{#fields}}
+   <label for="{{id}}">
+       <input id="{{id}}" type="radio" value="{{value}}" name="{{name}}" class="{{class}}" {{#checked}}checked{{/checked}}>
+       {{label}}
+   </label>
+{{/fields}}
+</div>
diff --git a/user/tests/behat/user_permission.feature b/user/tests/behat/user_permission.feature
new file mode 100644
index 00000000000..a8375371c6d
--- /dev/null
+++ b/user/tests/behat/user_permission.feature
@@ -0,0 +1,24 @@
+@core @core_user @javascript
+Feature: The admin can check student permission in moodle system.
+  In order to check permission of a user in moodle
+  As an admin user
+  I can searh student and see their permission
+
+  Background:
+    Given the following "users" exist:
+      | username | firstname | lastname | email             |
+      | user1    | User      | 1        | user1@example.com |
+
+  Scenario: The search setting is saved for each user.
+    Given I log in as "admin"
+    And I navigate to "Users > Permissions > Check system permissions" in site administration
+    And I follow "Search options"
+    And the field "from start" matches value "1"
+    And I click on "anywhere" "radio"
+    And I click on "Keep selected users, even if they no longer match the search" "checkbox"
+    And I click on "If only one user matches the search, select them automatically" "checkbox"
+    And I reload the page
+    Then the field "from start" matches value "0"
+    And the field "anywhere" matches value "1"
+    And the field "Keep selected users, even if they no longer match the search" matches value "1"
+    And the field "If only one user matches the search, select them automatically" matches value "1"
diff --git a/user/upgrade.txt b/user/upgrade.txt
index 292ca7d6426..e20f6c07300 100644
--- a/user/upgrade.txt
+++ b/user/upgrade.txt
@@ -22,6 +22,9 @@ This files describes API changes for code that uses the user API.
   - `user_get_participants`
   - `user_get_participants_sql`
   - `user_get_total_participants`
+* The users_search_sql function parameter $searchanywhere has been change to $searchtype for different type of search. $searchtype is a int parameter and has three constant value:
+  USER_SEARCH_STARTS_WITH: 0, USER_SEARCH_CONTAINS: 1, USER_SEARCH_EXACT_MATCH: 2
+  users_search_sql('User Test 2', '', false) =>  users_search_sql('Test Street', '', USER_SEARCH_CONTAINS)
 
 === 4.2 ===