Person A: Logged into iMessage on OS X Lion with same account as synced with iPhone
Person A sends iMessage from app to Person B. Person B responds
Conversation is not synced to iPhone. Person A sends another message to Person B from iPhone this time. It appears to Person B as a different message thread. However the same contact is seen for both.
I think I have found a solution to the problem. I don't mean to been too basic if everyone already knows this, but I'm sure some people out there are having trouble understanding.
The disconnect arises from the ways in which iMessage can send messages. It can either send it via your phone number or your email address. Most peoples' iPhones are probably set up to use their phone numbr while your Mac, iPad, or iPod touch can only use your email address. When this is the case, iMessage will interpret a message coming from each device as a distinct user. This leads it to create two message threads for the recepient. This is why the conversations will not sync.
The solution is, in fact, quite simple; You must configure your iPhone to send iMessages via your email account. The steps to do so are shown below.
1. Sign into iMessage using your Apple ID: Settings > Messages > Receive At > Use your Apple ID for iMessage > Input Account Information > Next
2. Ensure that Caller ID is set to your email address, not your phone number: Settings > Messages > Receive At > Caller ID
I hope this helps!