JFBConnect supports Open Graph Actions, which would normally have been the way to have content like you mention to automatically post to a user's Facebook account. However, Facebook recently removed the ability to use custom Open Graph Actions, so you can only use a handful of standard objects and actions and they don't support all the content types your users may share.
The only thing I can suggest for now is to use the Facebook Like and/or Share buttons in the JomSocial stream template files. With JFBConnect, adding the social buttons is pretty easy by adding tags like the below to the template files:
{SCFacebookLike}
{SCFacebookShare}
{SCTwitterShare}I hope that helps give you some ideas on how to start, but if you need anything else, please let us know.
Thanks,
Alex