Right now, I believe shared links are filtered out. The reason we don't show it is because links don't usually have a message to go along with them, which we need for the post to display.
If you want to test showing more stories, you can edit the /components/com_jfbconnect/libraries/provider/facebook/channel/page.php file. Around line 96, you'll see:
if(array_key_exists('from', $data) && array_key_exists('message', $data) && ($this->options->get('show_admin_only') == 0 || $data['from']['id'] == $pageId))
Change that to:
if(array_key_exists('from', $data) && ($this->options->get('show_admin_only') == 0 || $data['from']['id'] == $pageId))
That will remove the check to make sure there is a message in the post. However, you'll need to make sure that doesn't have any unwanted effects.
While you're testing, please set the "Enable Debug Mode" setting in JFBConnect to 'Yes'. That will disable caching so that the feed will be reloaded on every page load.
I hope that helps,
Alex