Q: Is there a solution for the pop3 problem?
A: Might be - backup first and do this at your own risk!
Do this at your own risk. BACKUP FIRST! Theoretically, you can convert your pop3 account to a imap account and let your client program resync all your email messages from your local computer to the server. Then do a normal imap migration.
Please note, this involves the chance of losing all your email data. Do this only if you know what you are doing!
If you are unsure, don't try to convert your POP3 account into IMAP. Really ... DON'T.