Are you using a separate extension for SEF URLs on your site? If so, please make sure it's set to 'skip' URLs for JFBConnect.
From what I can see, my guess is that some of the query parameters from Google are being stripped off the URL and it's preventing the authentication process from proceeding.
If that doesn't help, or you're using the standard Joomla SEF URLs, then please go to the JFBConnect -> Configuration area and set "Enable Debug Mode" to "Yes". Then, there may be extra error messages that appear during logging in. If so, let us know what those are.
Thanks,
Alex