Hi Tue,
That's fixable. Here's how.
Now that your server domain is mycompany.xx, do this :-
ping mail.f1-support.dk
From this you should be able to get the IP address of the ISP's mail server assigned to handle your e-mails.
Now, reconfigure your SME server to your proper domain name (ie. f1-support.dk).
From a web browser, get to the server manager and click on Hostnames and Addresses. Look for the entry mail and click on modify.
Assuming your are using SME 5.1.2, change location to Remote and enter the ISP mail server IP address you got from above into the line called Global IP then click on Modify.
That should do it. To test, ping mail.f1-support.dk and you should get the IP address of the ISP's mail server.
Let me know how you go.
Kelvin