Right now, JFBConnect doesn't have a way to automatically post content from your site back to a Facebook Page or Group. That's something we're planning to add later this year, likely in the 6.2 release, around late July.
Until then, we could provide you with the small bit of code that is used to push a post to a Facebook Group (once you have the Channel configured in JFBConnect). You'd need to implement that code in JomSocial, or wherever you want the post to be generated.
In the 6.1 release (early June), we'll have a method to fully display the contents of a Facebook Page, Group or other channel in a customizable format on your site.
I hope that helps explain,
Alex
jomsocial activity to facebook group
