The best way to move students between sets is to keep them in both the new class and the old class so scores are not lost. Be careful, if you delete that student from the old class, then their scores will be deleted too.

If you wish then to manually add those old scores into the new class for that child, go to gradebook for the new class, click 'Add', type in 'Name' (of the assessment), 'points' (total points), then select the student using the tick box and type in their 'grade' (score) and click 'submit'. The score you have entered for them will now appear in their list of test scores when you click their name. However, the scores you have entered won't appear in the class gradebook for the new class (as this would leave blanks for all other students, which doesn't look very neat).