Hi,
The Process.
Enable Messages on the iPhone.
Once the Number has Verified it can Send and Receive iMessages To and From the iPhone Number.
Enable the corresponding app on the Mac and set up the iMessages account with an Apple ID.
Once this has Verified you can send and receive iMessages to the Apple ID on the Mac.
Now you add the Apple ID to the iPhone Settings.
This will cause a pop up on the Mac to say the iPhone is using the iPhone Number AND the Apple ID
Accepting the Pop up Adds the iPhone Number to the Receive At list on the Mac and shows the Start conversations From drop down option.
From this Point on the iMessages sent to either Apple ID or Phone number will appear on the other device.
Once Received on Registered devices the iMessages are deleted from the Servers. (they are Pushed from the servers to specific devices so when one is off line or unattainable the servers will keep trying until the iMessages is Accepted or it times out).
If you add a third device it will only "Sync" (Display on all devices) from that point onwards.
It cannot be made to get older iMessages as they no longer exist.
9:46 pm Thursday; February 26, 2015
iMac 2.5Ghz i5 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