Small addendum to Christian's message:
[1] GMX used to restrict IMAP access to "Premium"/paying customers. If that's still the case you will have to have use POP3 rather than IMAP for incoming mail (i.e. it will retrieve messages from your GMX inbox but won't replicate your folder tree in your local mailbox):
Incoming mail:
Server: pop.gmx.net
Port: 995
SSL: SSL
Outgoing mail:
Server: mail.gmx.net
Port: 587
SSL: STARTTLS
[2] I had to unclick the "Use non-blocking SSL" option in the account preferences to make it work with GMX (the screenshot is taken from a different "flavor" of the Sylpheed email client but I believe this dialog looks the same in Navigatrix version):
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