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No it doesn't, you need to impersonate an user and login with your password in order to relay messages outside of FB messenger. That said, it has been done: https://github.com/tulir/mautrix-facebook

No, it used to support XMPP, but that support was eventually removed: https://news.ycombinator.com/item?id=9266769

I knew about that: the talk of MQTT made me think that there was some improvement in the situation.

I wouldn't call it that, but this might be usable for you: https://github.com/dequis/purple-facebook

Or maybe not: https://github.com/dequis/purple-facebook/issues/496

https://www.facebook.com/notes/facebook-engineering/building...

It is based on MQTT+extensions.