Hi,
I would then point out h5c8h's remarks about checking everything on the iPhone.
I would go a step further.
1) Is the iPhone using OS 6 at least ?
2) In Settings > Messages > Send and Receive is the Apple ID AND the iPhone Number ticked to say they are active ?
3) In the "Send From" spot is the iPhone using the same option as the Mac version of the app ?
(in my opinion this should not matter but I have seen posts to say it does).
If at that point all seems to be in place I would place the iPhone in Airplane Mode to break with the server.
After a few minutes wait I would take the iPhone out of Airplane Mode and restart the App on the Mac.
This Should get the pop up messages from the server to say the iPhone is using the iPhone Number and the Apple ID which you should use the Accept button on.
If that does not have any effect remove the Apple ID on the iPhone before placing in Airplane Mode and Adding it back after taking it out of Airplane mode (Effectively resetting Messages)
7:43 PM Friday; May 3, 2013
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.3)
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