However, why the transfer with FileZilla works with this server?
I do not know. The server bug may manifest only in some very specific situations.
For example FileZilla uses SFTP version 3. While WinSCP is capable of SFTP up to version 6.
You can try forcing WinSCP to use version 3:
Great hint! It works! Thanks a lot for your help!
I informed the webmaster of the server too.