Moving Test Cases from one project to another

There's no feature to help with this, but as to thoughts on how to achieve:

1. my first check would be to see if I could clone the Jira Project and thereby clone the Scale setup also, but I'm not confident that would work.
2. Next I'd check Test Case export options and see if the export data contains the folder structure.  If it does then you should be able to edit the data and import using that folder data to automatically create the folder structure as well as import your test cases.
3. After that I'd look at the API and the Folder endpoint to see what I could do with that.

Hopefully one of those options works for you.