JFBConnect fires the normal Joomla user plugins when a user logs in. CB also fires off the normal Joomla plugins, as far as we know. Is there any reason you can't change your CB-specific plugin to be a Joomla user plugin? Then, it will work for JFBConnect, or any other authentication mechanism you may add in the future.
The other alternative would be to add your code to our User plugin, which we can help you do.. but you'd have to make that change with any update.
Let us know if you need more information, and we'll do what we can to help!
JFBConnect Login Process
