> The same email sent directly from the sender address arrived.

Based on this, there are two lines of investigation that are worth pursing:

One key difference is the sender envelope from address (different from the From: address in the message itself). A CiviMail message sent from CiviCRM uses the domain in the mail account used for bounce processing.

i.e. look at [yourdomain]/civicrm/admin/mailSettings?reset=1 and look at the row that says "Used for bounce processing".

So, your first line of inquiry is to look at the SPF record of that domain and make sure that the machine that sends out the email has an entry in some form, i.e. that your smtp server ip is blessed to send out mail from that domain.

If that has already been done properly, then the second line of inquiry is to look at the IP of your smtp machine and look at it's reputation. It's possible that the GMX is using a blacklist to block email from your ip.

If both of those seem like issues that are too technical, then you really will need someone who understands them to sort it out, otherwise you won't be getting much value from CiviMail.