I think you can do this:
Backup your e-mails in case you break something. Backup them outside Thunderbird.
Add a new account to Thunderbird connected to your www.gmx.ch inbox with IMAP. This way you should now have 2 accounts in Thunderbird connected to your www.gmx.ch inbox: one with IMAP and one with POP3.
Now change the password to the www.gmx.ch inbox ...
If you want to get hold of MIME parts that don't have filenames, e.g. the text and HTML, then try
sudo apt install maildir-utils
mu extract source.eml --save-all