Kayo I don't think this extension can implement that.
If this extension is OAuth compatible maybe you can use the Laravel Passport extension on the client forum. But I'm not sure if it's only Wordpress compatible (?)
If you only need existing users up until now to exist in the new forum, you can just copy over the user records as suggested by mrnemesys New users on forum 1 won't have their profile available on forum 2 though.
To keep the tables in sync might require using database views, or altering one of your Flarum to use the users
table of the other install. We don't currently have any extension handling that.