HI,
On the iPhone clear all Messages.
If you want to "Save" some use the Edit button in an Open conversation and highlight/select all items and then Use th Forward button and send to your Apple ID in Messages.
You lose formatting but you will have the details
Next Add the Apple ID to Settings > Messages > Received At > Caller ID
This bit with the cleared Messages links the Apple ID and iPhone Number so that Messages sent to the Phone are synced to the devices and Messages app that use the Apple ID.
8:42 PM Wednesday; July 25, 2012
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Lion 10.7.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
"Limit the Logs to the Bits above Binary Images." No, Seriously