If the student does not yet have a NoodleTools account under the school, create one (with a different username than the MLA Lite account) and sign into it once.
Log out of the new account and log in to the MLA Lite account.
On the Projects screen, mark the checkboxes next to each project, then click "Copy" from the menu that comes up. Choose the option to copy the projects to another user's account and enter the ID associated with the new user account.
Log out of the MLA Lite account and log in to the new account. You should find the copied project(s) there, where you can resume work on them.