Hi Infinite Vortex, thanx for your reply! When I tried this yesterday it did not work, all accounts gave the offline sign next to it in the mail client, so I guessed this was due to the wrongly configured domain.
Today I changed the DNS Zone entry on the Mac to the new IP of the machine on the local network. After your reply, I tried to restart the Mac and the mail service, and now it does work! Whatever it was, your reaction led me to solve my problem so many thanx for that!