Need some advice on integrating Ruby on Rails website to a forum login

So i am trying to set up a subdomain with a forum for my ruby on rails website which will be hosted on different server.

so I have A domain.com hosted on AWS which is built with Ruby On rails

then B Community.domain.com hosted on another server.

I would like to make community.domain.com a forum, options would be SMF, Mybb, phpbb, or other.

Question:
Any advice which forum software i could use so that they log in on my website A and still logged in when accessing B or how I would even go...

Need some advice on integrating Ruby on Rails website to a forum login

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