Why Do Some Messages Come To iPhone But Not Mac In OS X Mountain Lion?
The first step is to make sure that your Apple ID for Messages for Mac and the Apple ID you use for iCloud on your iPhone are spelled exactly the same way. On your iPhone you should also go to Settings > Messages > Receive At and make sure it says "2 Addresses". Both your phone number and Apple ID should be listed. Once that is squared away, your conversations should be in sync.