This is how I configure delivery of e-mail generated on “sattelite” machines.

On SMTP relaying server, edit /etc/postfix/helo_access:

# postmap helo_access
a_random_name_known_by_server_and_client1_only      PERMIT
a_random_name_known_by_server_and_client2_only      PERMIT

To update the database file format used by postfix, run postmap helo_access. The file must then specify:

smtpd_recipient_restrictions =
check_helo_access hash:/etc/postfix/helo_access

On each “clientX” or sattelite system, specify myhostname as a_random_name… reload/restart postfix, and everything should be up and running.