We've definitely added a lot more integration between Facebook Groups and Joomla since 2014. However, I'm not specifically sure what integration you're looking for.. there's lots of ways that integration can occur.
What JFBConnect does support is the automatic posting of content to your Facebook Group. That content must come from an extension that we have a supporting Open Graph plugin for, which currently includes Joomla content, K2 items, JomSocial, EasySocial and some others.
JFBConnect can also pull in the feed from your Facebook Group and show it using our Social Stream module, like you see in the bottom of this page. We show our Facebook Page, Twitter Feed and LinkedIn Company Feed using the social stream module.
So, we do have methods to push content to your group and pull your feed in. If you need a tight integration where a Group post creates a forum thread that the discussion continues on or something, we don't support that. It's near impossible to do some forms of integration because, while we can pull a post in from a Group, let's say, we can't push comments back to it from your users.. so comments on the original post and new posts to your forum thread, for instance, would be completely separate.. which most likely would confuse things further.
Even more, especially with Groups, some privacy restrictions need to be considered. If your Group has privacy enabled, publicly showing that feed on your site could be a problem for users who expect their posts to only be seen by the group itself.
That's not to say we wouldn't do further integration between social network feeds and JFBConnect. We'd love to hear specifically what you're looking for and have made many great strides toward deeper integration with the last few releases, and would love to do more.
Thanks,
Alex