Unfortunately, the Database activity doesn't export files. Then you'd have to make a course backup of just the database, include the enrolled users and then restore into the other course.
An alternative would be the Student folder plugin. At the end of the year, you can just download it to a .zip file and upload it as a regular folder on your other course.
If you trust your students with being able to edit other students' contributions, you can also just use a regular Moodle folder resource and change the permissions to allow students to edit it.