Thanks, Hal.
So I followed the procedure described there and changed two things in my
configuration:
* I changed the account in Control Panel/Services/Fax Service from
LocalSystem to my account
* In Fax Service Management Console/Devices I added 'Send to Local
e-mail inbox"

After that the situation with Outlook improved. When sending a fax
message the modem now gets a short request (but doesn't dial) and I
receive a message in Outlook from system administrator "The Fax
transport service failed to deliver the message to this recipient."

The fax number to dial is stored in the Contacts File within Outlook and
has the format +xx (yyy) zzzzzzz. For sending the fax I'm creating an
new e-mail message and selecting the entry with e-mail-type FAX from the
Adress Book.

Is there any log file that shows a more detailed version of the reported
problem?