I'm not sure exactly how Joomdle's authentication works. I can tell you how JFBConnect works though. The problem with integrating into other systems is generally that JFBConnect doesn't have a username and password for the user that is authenticating. All we have is a 'token' from Facebook that says user "John Smith" successfully logged in. We then tell Joomla to log that user in. We do trigger all of the standard Joomla User and authentication plugins and those plugins shouldn't need to see a username or password, they should just take a JUser object and trust that that user has successfully logged into Joomla and do whatever the extension needs to do to log the user in.
If Joomdle requires a username and password to log the user into the Moodle system, then that's not going to work with JFBConnect. One test you can try, that is unrelated to JFBConnect, is simply enable the Gmail - Authentication plugin that comes with Joomla. Test to see if that properly logs you into Joomdle. If not, that means that Joomdle is expecting a username and password (or they have specific integration with the Gmail Authentication plugin).
I went through their
integration documentation
, but couldn't find any documentation about calling their SSO API. If there is something they can point us to, we'd gladly look into it further. We'd also have no problem providing a developers copy of JFBConnect to them.
Hope that helps get you started on investigating things.
Thanks,
Alex