Thanks for your replies. Unfortunately we are currently using a shared hosted Exchange platform, so there is no way to configure a relay on that side.
What's strange is that there is a parameter (SMTP_TECH_SENDER) for a fixed sender, but I don't know what this technical sender is good for, as for the real sender still the address of the user is taken. So if anybody knows whether there is a parameter which influences that I woul be very thankful !
BR,
Martin