So Messages App on the Mac has been set up with the Apple ID for the iMessages Account.
First iMessages cannot be sent from the Mac but once the iPhone has sent an iMessage and the sync version appears on the Mac you an send from the Mac ?
Have I understood that correctly ?
I have seen people post with issues about Sending iMessages from the Mac.
However the "trick" of starting the Chat on the iPhone is a new twist.
I would try a PRAM reset.
Shut down the computer.
Restart it holding down Apple/CMD ( or ⌘)+ALT( ⌥)+P+R Keys until you have heard three Start Up Bongs.
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad
"Limit the Logs to the Bits above Binary Images." No, Seriously