No worries, and thanks for answer!
To transfer the site i have used the all-in-one-migration plugin. Everything else (site and all the other plugins) is working totally fine.
After the transfer i updated your plugin, entered the new licence key and changed the root path (this was the only thing that really had to be changed manually). But the listing of the files is still not working.
I can also create a new download package with some items in it -> the zip can be downloaded, the page with the items list is empty.