How to transfer iMessages on my Mac to my new iPhone?

I have the iMessage app on my Mac and I'd like to transfer all of my conversations onto my new phone (iPhone 6). Is this even possible?

Technically no, but you can still transfer the messages. The iMessage app on OS X connects to the one on iPhones (basically its the same app) so just signing into it on the iPhone should bring them onto it as well.

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