Sedlak,
If it's actually a Facebook Group, and not a Page, there isn't a way to do this. Facebook restricts what you can do with groups quite heavily as they aren't usually meant to be 'public' areas. With Facebook Pages, it's possible to post content to your wall, but JFBConnect doesn't currently support the ability to do that. It's something we're planning to do later this year.
The same is true with the JFBCFan module, which lets you show the stream of your Fan Page in your site. It only works with Pages, not with groups.
Hope that helps explain, but if you have any more questions, let us know,
Alex
Facebook group
