diff --git a/lib/questionlib.php b/lib/questionlib.php
index f8abcf56fb7..0cd76b49fa6 100644
--- a/lib/questionlib.php
+++ b/lib/questionlib.php
@@ -667,16 +667,17 @@ function move_question_set_references(int $oldcategoryid, int $newcatgoryid,
     if ($delete || $oldcontextid !== $newcontextid) {
         $setreferences = $DB->get_recordset('question_set_references', ['questionscontextid' => $oldcontextid]);
         foreach ($setreferences as $setreference) {
-            $filter = json_decode($setreference->filtercondition);
-            if (isset($filter->questioncategoryid)) {
-                if ((int)$filter->questioncategoryid === $oldcategoryid) {
-                    $setreference->questionscontextid = $newcontextid;
-                    if ($oldcategoryid !== $newcatgoryid) {
-                        $filter->questioncategoryid = $newcatgoryid;
-                        $setreference->filtercondition = json_encode($filter);
-                    }
-                    $DB->update_record('question_set_references', $setreference);
+            $filter = json_decode($setreference->filtercondition, true);
+            if (isset($filter['questioncategoryid'])) {
+                $filter = question_reference_manager::convert_legacy_set_reference_filter_condition($filter);
+            }
+            if ((int)$filter['filter']['category']['values'][0] === $oldcategoryid) {
+                $setreference->questionscontextid = $newcontextid;
+                if ($oldcategoryid !== $newcatgoryid) {
+                    $filter['filter']['category']['values'][0] = $newcatgoryid;
+                    $setreference->filtercondition = json_encode($filter);
                 }
+                $DB->update_record('question_set_references', $setreference);
             }
         }
         $setreferences->close();
@@ -728,6 +729,7 @@ function question_move_category_to_context($categoryid, $oldcontextid, $newconte
 
     $subcatids = $DB->get_records_menu('question_categories', ['parent' => $categoryid], '', 'id,1');
     foreach ($subcatids as $subcatid => $notused) {
+        move_question_set_references($subcatid, $subcatid, $oldcontextid, $newcontext->id);
         $DB->set_field('question_categories', 'contextid', $newcontextid, ['id' => $subcatid]);
         question_move_category_to_context($subcatid, $oldcontextid, $newcontextid);
     }
diff --git a/lib/tests/questionlib_test.php b/lib/tests/questionlib_test.php
index ead871f8f93..fdedc8ce57e 100644
--- a/lib/tests/questionlib_test.php
+++ b/lib/tests/questionlib_test.php
@@ -17,6 +17,7 @@
 namespace core;
 
 use core_question\local\bank\question_bank_helper;
+use mod_quiz\quiz_settings;
 use question_bank;
 
 defined('MOODLE_INTERNAL') || die();
@@ -1673,4 +1674,109 @@ final class questionlib_test extends \advanced_testcase {
 
     }
 
+    /**
+     * Update the context for a set reference, keeping the original category.
+     *
+     * @covers ::move_question_set_references()
+     */
+    public function test_move_question_set_references_context(): void {
+        $this->setAdminUser();
+        // Create a course with a quiz containing a random question from a qbank context.
+        $randomcourse = self::getDataGenerator()->create_course(['shortname' => 'Random']);
+        $qbank1 = self::getDataGenerator()->get_plugin_generator('mod_qbank')->create_instance(['course' => $randomcourse->id]);
+        $context1 = \context_module::instance($qbank1->cmid);
+        $qbank2 = self::getDataGenerator()->get_plugin_generator('mod_qbank')->create_instance(['course' => $randomcourse->id]);
+        $context2 = \context_module::instance($qbank2->cmid);
+        $topcategory = question_get_top_category($context1->id, true);
+        $randomcategory = self::getDataGenerator()->get_plugin_generator('core_question')->create_question_category(
+            ['parent' => $topcategory->id],
+        );
+        $randomquiz = self::getDataGenerator()->get_plugin_generator('mod_quiz')->create_instance(
+            [
+                'course' => $randomcourse->id,
+                'grade' => 100.0,
+                'sumgrades' => 2,
+                'layout' => '1,0',
+            ],
+        );
+
+        $randomquizsettings = quiz_settings::create($randomquiz->id);
+        $structure = $randomquizsettings->get_structure();
+
+        $filtercondition = [
+            'filter' => [
+                'category' => [
+                    'jointype' => \core_question\local\bank\condition::JOINTYPE_DEFAULT,
+                    'values' => [$randomcategory->id],
+                    'filteroptions' => ['includesubcategories' => true],
+                ],
+            ],
+        ];
+        $structure->add_random_questions(1, 1, $filtercondition);
+        $structure = $randomquizsettings->get_structure();
+        $randomquestion = $structure->get_question_in_slot(1);
+
+        $this->assertEquals($randomquestion->contextid, $context1->id);
+        $this->assertEquals($randomquestion->filtercondition['filter']['category']['values'][0], $randomcategory->id);
+
+        move_question_set_references($randomcategory->id, $randomcategory->id, $context1->id, $context2->id);
+
+        $structure = $randomquizsettings->get_structure();
+        $randomquestion = $structure->get_question_in_slot(1);
+
+        $this->assertEquals($randomquestion->contextid, $context2->id);
+        $this->assertEquals($randomquestion->filtercondition['filter']['category']['values'][0], $randomcategory->id);
+    }
+
+    /**
+     * Update the context and category for a set reference.
+     *
+     * @covers ::move_question_set_references()
+     */
+    public function test_move_question_set_references_category(): void {
+        $this->setAdminUser();
+        // Create a course with a quiz containing a random question from a qbank context.
+        $randomcourse = self::getDataGenerator()->create_course(['shortname' => 'Random']);
+        $qbank1 = self::getDataGenerator()->get_plugin_generator('mod_qbank')->create_instance(['course' => $randomcourse->id]);
+        $context1 = \context_module::instance($qbank1->cmid);
+        $qbank2 = self::getDataGenerator()->get_plugin_generator('mod_qbank')->create_instance(['course' => $randomcourse->id]);
+        $context2 = \context_module::instance($qbank2->cmid);
+        $topcategory1 = question_get_top_category($context1->id, true);
+        $topcategory2 = question_get_top_category($context2->id, true);
+        $randomquiz = self::getDataGenerator()->get_plugin_generator('mod_quiz')->create_instance(
+            [
+                'course' => $randomcourse->id,
+                'grade' => 100.0,
+                'sumgrades' => 2,
+                'layout' => '1,0',
+            ],
+        );
+
+        $randomquizsettings = quiz_settings::create($randomquiz->id);
+        $structure = $randomquizsettings->get_structure();
+
+        $filtercondition = [
+            'filter' => [
+                'category' => [
+                    'jointype' => \core_question\local\bank\condition::JOINTYPE_DEFAULT,
+                    'values' => [$topcategory1->id],
+                    'filteroptions' => ['includesubcategories' => true],
+                ],
+            ],
+        ];
+        $structure->add_random_questions(1, 1, $filtercondition);
+        $structure = $randomquizsettings->get_structure();
+        $randomquestion = $structure->get_question_in_slot(1);
+
+        $this->assertEquals($randomquestion->contextid, $context1->id);
+        $this->assertEquals($randomquestion->filtercondition['filter']['category']['values'][0], $topcategory1->id);
+
+        move_question_set_references($topcategory1->id, $topcategory2->id, $context1->id, $context2->id);
+
+        $structure = $randomquizsettings->get_structure();
+        $randomquestion = $structure->get_question_in_slot(1);
+
+        $this->assertEquals($randomquestion->contextid, $context2->id);
+        $this->assertEquals($randomquestion->filtercondition['filter']['category']['values'][0], $topcategory2->id);
+    }
 }
diff --git a/mod/qbank/classes/task/transfer_question_categories.php b/mod/qbank/classes/task/transfer_question_categories.php
index 2313bd5a68c..ec20fc5cad7 100644
--- a/mod/qbank/classes/task/transfer_question_categories.php
+++ b/mod/qbank/classes/task/transfer_question_categories.php
@@ -171,6 +171,8 @@ class transfer_question_categories extends adhoc_task {
 
         $newtopcategory = question_get_top_category($newcontext->id, true);
 
+        move_question_set_references($oldtopcategory->id, $newtopcategory->id, $oldtopcategory->contextid, $newcontext->id, true);
+
         // This function moves subcategories, so we have to start at the top.
         question_move_category_to_context($oldtopcategory->id, $oldtopcategory->contextid, $newcontext->id);
 
diff --git a/mod/qbank/tests/task/transfer_question_categories_test.php b/mod/qbank/tests/task/transfer_question_categories_test.php
index a3af54d9871..9418282e91d 100644
--- a/mod/qbank/tests/task/transfer_question_categories_test.php
+++ b/mod/qbank/tests/task/transfer_question_categories_test.php
@@ -21,6 +21,8 @@ use context_course;
 use context_coursecat;
 use context_module;
 use context_system;
+use core_question\local\bank\random_question_loader;
+use mod_quiz\quiz_settings;
 use stdClass;
 use core_question\local\bank\question_version_status;
 
@@ -159,6 +161,30 @@ final class transfer_question_categories_test extends \advanced_testcase {
         quiz_add_quiz_question($question1->id, $quiz, 1);
         quiz_add_quiz_question($question2->id, $quiz, 1);
 
+        // Create a course with a quiz containing a random question from the system context.
+        $randomcourse = self::getDataGenerator()->create_course(['shortname' => 'Random']);
+        $randomquiz = $quizgenerator->create_instance(
+            [
+                'course' => $randomcourse->id,
+                'grade' => 100.0,
+                'sumgrades' => 2,
+                'layout' => '1,0',
+            ],
+        );
+        $randomquizsettings = quiz_settings::create($randomquiz->id);
+        $structure = $randomquizsettings->get_structure();
+        $topcategory = $DB->get_record('question_categories', ['contextid' => $sitecontext->id, 'parent' => 0]);
+        $filtercondition = [
+            'filter' => [
+                'category' => [
+                    'jointype' => \core_question\local\bank\condition::JOINTYPE_DEFAULT,
+                    'values' => [$topcategory->id],
+                    'filteroptions' => ['includesubcategories' => true],
+                ],
+            ],
+        ];
+        $structure->add_random_questions(1, 1, $filtercondition);
+
         // Create a course category and then a question category attached to that context.
         $coursecategory = self::getDataGenerator()->create_category();
         $this->coursecatcontext = context_coursecat::instance($coursecategory->id);
@@ -275,6 +301,20 @@ final class transfer_question_categories_test extends \advanced_testcase {
         $question4 = $questiongenerator->create_question('shortanswer', null, ['category' => $unusedcategory->id]);
         $quiz = $quizgenerator->create_instance(['course' => $course->id, 'grade' => 100.0, 'sumgrades' => 2, 'layout' => '1,0']);
         quiz_add_quiz_question($question1->id, $quiz, 1);
+
+        // The quiz also contains a random question from the used category.
+        $quizsettings = quiz_settings::create($quiz->id);
+        $structure = $quizsettings->get_structure();
+        $filtercondition = [
+            'filter' => [
+                'category' => [
+                    'jointype' => \core_question\local\bank\condition::JOINTYPE_DEFAULT,
+                    'values' => [$usedcategory->id],
+                    'filteroptions' => ['includesubcategories' => false],
+                ],
+            ],
+        ];
+        $structure->add_random_questions(1, 1, $filtercondition);
     }
 
     /**
@@ -305,6 +345,24 @@ final class transfer_question_categories_test extends \advanced_testcase {
         $this->assertEquals($parentcat->id, $parentcatq->categoryid);
         $this->assertEquals($childcat->id, $childcatq->categoryid);
 
+        // Make sure the "Random" course has 1 quiz with 1 random question that returns the questions from the system top category.
+        $randomcourse = $DB->get_record('course', ['shortname' => 'Random']);
+        $coursemods = get_course_mods($randomcourse->id);
+        $randomquiz = reset($coursemods);
+        $randomquizsettings = quiz_settings::create($randomquiz->instance);
+        $structure = $randomquizsettings->get_structure();
+        $randomquestionslot = $structure->get_question_in_slot(1);
+        $this->assertEquals($randomquestionslot->contextid, $sitecontext->id);
+        $loader = new random_question_loader(new \qubaid_list([]));
+        $randomquestions = $loader->get_filtered_questions($randomquestionslot->filtercondition['filter']);
+        $this->assertCount(2, $randomquestions);
+        $randomq1 = reset($randomquestions);
+        $randomq2 = end($randomquestions);
+        $this->assertEquals($parentcatq->id, $randomq1->id);
+        $this->assertEquals($parentcat->id, $randomq1->category);
+        $this->assertEquals($childcatq->id, $randomq2->id);
+        $this->assertEquals($childcat->id, $randomq2->category);
+
         // Make sure that the course category has a question category below 'top'.
         $allcoursecatcats = $DB->get_records('question_categories', ['contextid' => $this->coursecatcontext->id], 'id ASC');
         $this->assertCount(2, $allcoursecatcats);
@@ -360,6 +418,15 @@ final class transfer_question_categories_test extends \advanced_testcase {
         $this->assertCount(2, $this->get_question_data([$unusedcat->id]));
         $emptycat = next($questioncats);
         $this->assertCount(0, $this->get_question_data([$emptycat->id]));
+
+        // The question reference for the random question is using the "used" category, and the site context.
+        $coursemods = get_course_mods($this->usedunusedcontext->instanceid);
+        $quiz = reset($coursemods);
+        $quizsettings = quiz_settings::create($quiz->instance);
+        $structure = $quizsettings->get_structure();
+        $randomquestionslot = $structure->get_question_in_slot(2);
+        $this->assertEquals($this->usedunusedcontext->id, $randomquestionslot->contextid);
+        $this->assertEquals($usedcat->id, $randomquestionslot->filtercondition['filter']['category']['values'][0]);
     }
 
     /**
@@ -410,6 +477,22 @@ final class transfer_question_categories_test extends \advanced_testcase {
         $this->assertEquals($topcat->id, $parentcat->parent);
         $this->assertEquals($parentcat->id, $childcat->parent);
 
+        // The random question should now point to the questions in the site course question bank.
+        $randomcourse = $DB->get_record('course', ['shortname' => 'Random']);
+        $coursemods = get_course_mods($randomcourse->id);
+        $randomquiz = reset($coursemods);
+        $randomquizsettings = quiz_settings::create($randomquiz->instance);
+        $structure = $randomquizsettings->get_structure();
+        $randomquestionslot = $structure->get_question_in_slot(1);
+        $this->assertEquals($randomquestionslot->contextid, $sitemodcontext->id);
+        $loader = new random_question_loader(new \qubaid_list([]));
+        $randomquestions = $loader->get_filtered_questions($randomquestionslot->filtercondition['filter']);
+        $this->assertCount(2, $randomquestions);
+        $randomq1 = reset($randomquestions);
+        $randomq2 = end($randomquestions);
+        $this->assertEquals($parentcat->id, $randomq1->category);
+        $this->assertEquals($childcat->id, $randomq2->category);
+
         // Course category context checks.
 
         // Make sure that the course category has no question categories, not even 'top'.
@@ -525,6 +608,19 @@ final class transfer_question_categories_test extends \advanced_testcase {
         $this->assertEmpty($this->get_question_data([$usedunusedcats['top']->id]));
         $this->assertCount(2, $this->get_question_data([$usedunusedcats['Used Question Cat']->id]));
         $this->assertCount(2, $this->get_question_data([$usedunusedcats['Unused Question Cat']->id]));
+
+        // The question reference for the random question is using the same category, but the new context.
+        $modinfo = get_fast_modinfo($this->usedunusedcontext->instanceid);
+        $quizzes = $modinfo->get_instances_of('quiz');
+        $quiz = reset($quizzes);
+        $quizsettings = quiz_settings::create($quiz->instance);
+        $structure = $quizsettings->get_structure();
+        $randomquestionslot = $structure->get_question_in_slot(2);
+        $this->assertEquals($usedunusedqbank->context->id, $randomquestionslot->contextid);
+        $this->assertEquals(
+            $usedunusedcats['Used Question Cat']->id,
+            $randomquestionslot->filtercondition['filter']['category']['values'][0]
+        );
     }
 
     public function test_fix_wrong_parents(): void {