Hi!
I've the problem, that imessage is working on all devices, two iPhones and one ipad, but stopped working on my Macbook Pro (MacBook Pro Retina, 13', Mitte 2014) on 12.02.2017, 23:53. At that time I was using 10.12.4 Beta (16E144f) for 12 days without iMessage-Problems.
Googling lead me to an older post in the apple-forum.:
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If you have the Serial Number showing on your computer and you have tried and Safe Boot and a NVRAM reset AND tested in another Mac user account on your Mac then you should phone Apple Support (Apple Care)
This can be long and tedious but it is the only way to reset the account.
Basically the App not only uses the Apple ID and Password to login but the Serial Number as well to prove it is "you".
There is no reset on the App so you have to call.
Level 1 responders and Script led and are trying to solve Apple Care issues.
You have an Apple ID issue (free to fix) and do not need to do all the tests they suggest.
Politely ask to speak to someone higher.
Level 2s may or may not know about the issue (judging by what other people have posted back).
Again they may want to run test with you and gather data (Apple know there is an issue but cannot find what is triggering it).
Updating, Upgrading and Reinstalling do not work as the issue is at the iMessage Server end.
Ask the Level 2 (or Higher) to look at the sever and check.
At this point they may involve the Engineers as it now seems they are the only ones allowed to reset the server.
You may get a messages that it will take 24 hours (or upto to 5 days) to reset.
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At this point I tried to talk to the "normal" support (here in Germany), because I`m ptretty shure, this problem has nothing to do with the Beta 1. But they told me, there is no support because I'm using a beta software and participate in the public beta Program :-(
The only possibility - to post this Problem at the Dev-Forum; and that's what I've done...
Cheers
Manfred