Edit /etc/mail/submit.cf so that the DS line contains the FQDN to your upstream mail server.
You'll also need to set root:smmsp permissions on /var/spool/mqueue.
Hope this saves someone else some time (it took a bit of reading on my part).
Update: this post was flagged (in June 2022) as violating Blogger's content policy (relating to Malware and Viruses). The above content has not been changed. Only this last statement has been added. Please note that the above post does not relate to Malware or Virsues.