We're looking into what may be happening here. There are multiple bug reports on Facebook about issues like this when importing Facebook Groups. Unfortunately, there's no consensus as to the issue, though it sounds like it's a privacy issue based on your friendship with the user sharing the content in addition to being just an admin of the Group.
However, looking at your Facebook Group, most of the content shared is publicly available (other websites or YouTube clips) and not really 'private' content.. so I'm unsure why it's like that.
We'll be trying to recreate the issue and see if we can determine the problem. There were no changes in the Group functionality in v6.1.1 or v6.1.2, so the issue doesn't have to do with those releases. It's likely something that just happened around the same time with Facebook or the Group itself.
I'm sorry for the delayed response. We've tried to recreate the issue, but haven't been able to. Unfortunately, we don't have any truly active groups to test with either, which may be part of the problem.
From everything I can tell, this seems to be an issue with Facebook, as noted above, and their privacy settings. I don't believe this has anything to do with upgrading JFBConnect as there were no changes in the 6.1.1 or 6.1.2 releases regarding the Groups feature. We'll gladly even send you the older 6.1.0 release if you'd like to re-install it and test if downgrading it fixes the problem.
It's strange that some posts work, and some don't. Again, all I can think is that there's a relationship between the user you set the Channel up with and the users that are posting in the group, but I'm at a bit of a loss.