Right, but, well, first, when you send a message the thing that goes into
the Sent Item isn't a message you 'receive', so the rule you created
initially would never work.

Second, I forget, when you select Sent through a specific account, does it
allow you to select the other Exchange mailbox?  I don't remember if I had
the ability when I had an Exchange server.  If it doesn't, you're pretty
much stuck with my Lastly or you need everyone to set up a second profile
and to log directly into the service mailbox.

Lastly, I had to do this type of configuration and never bothered with a
rule.  The users were instructed to move their sent items manually and to
simply view the Sent Items folder by From to more easily select the
messages.  It worked wonders actually.