Alex,
Do you have the Community Builder plugin for JFBConnect installed? You can check this on the JFBConnect administrator overview page. Also, make sure it's up-to-date and published (green check next to it).
Then, in the Profiles tab of JFBConnect, make sure that it's enabled for all logins and that the avatar import setting is enabled. If you have those things setup, then let me know if you're doing any sort of profile mapping from Facebook and if those user fields are properly being inserted into the user's CB profile.
All that will help narrow down the problem and come up with a good solution. If you find anything else out, let me know!
Problem......
