Currently Being ModeratedNov 15, 2013 2:05 PM (in response to shl93)
You have to have Computer running Mountain Lion (and therefore Messages 7.x.x.) or Mavericks and Messages 8 to be able to Sync the iPhone Messages app when it send iMessages to the Mac in an iMessages account set up in Messages.
To make it a little clearer.
iChat become Messages in Mountain Lion.
As well as the AIM and Jabber option and their variants such as some Apple IDs being valid AIM Screen Names and the Google Talk and Facebook chat option as Jabber variants the app has as iMessages account added.
The iMessages account on the Mac app is then set up using the same Apple ID as used on the iPhone and iMessages can then be synced (display on All devices).
iMac 2.5Ghz 5i 2011 (Mavericks 10.9)
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