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[Gaijin]

But they are still in the same databse?
If and if not you still can just write up a custom sql_query that will insert the needed things into myBB table
If they are not in the same db then you'll also need a new connection.

Just take a look on what data myBB saves upon the registration and copy that query based on your other form inputs.
For a login I would then check for the myBB cookie when loging the user into the Game.