Jim,
Very sorry for the delayed response. We still do not have any Facebook Group integration in JFBConnect and it's not something we have on our immediate radar to implement.
If you're using a Facebook Page (and not a Group), you could use the JFBCFan module, which is included in JFBConnect, to easily show the latest administrator posts to your Facebook Page. Facebook Pages are generally public though, so if you need privacy options, the Group may be what you need.
Finally, there are some ways, using JFBConnect, that you could fetch the group posts. However, it would take some PHP development, so you'd need a developer that could implement it. We can help with some tips, but wouldn't be able to do it all for you.
I hope that helps explain, but if you have any other questions, just let us know.
Thanks,
Alex