Ok.. we have a quick code-fix that should get you going. We need to do more investigation to make sure this won't break anything unexpectedly, but it seems to be working properly from initial testing.
To implement, please edit the /components/com_jfbconnect/libraries/provider/facebook.php file. Around line 171, you'll see:
$params['access_token'] = JFBCFactory::usermap()->getUserAccessToken($jid, 'facebook');
Change that to:
$params['access_token'] = $this->client->getToken();
Let us know how that goes and thanks for your patience!
Alex