Quick question, did you set the setting under Setup> Clients> Options to match the settings you changed under email options? It is the same setup in the top of the option page for both Email and Clients. Both will need to be set to the same setting for this to work. I hope this helps.
Can you provide screenshots with highlighted areas as to which settings are affected?
What's the earliest installed version of Web Help Desk within this server?
Okay... After fiddling around with the settings I somehow got it to work...
At first I tried to use the "only if e-mail matches an accepted domain"-option and added the external domain I wanted to test.
After that I simply set it to "Yes", deleted the client, tried again, and it worked.
lastly I deleted the accepted domains, deleted the client, tried again, and it worked.
I also deleted the default incoming and outgoing E-Mail-Accounts and set them to the ones I set up. (I don't know if that had any effect on it though.)
I hope this helps if anyone else ever encounters the same issue.