Bojan,
We don't do active testing with user syncing plugins, so I can't make any guarantees as to what 'currently' works or doesn't. For usersyncing in general, we'd recommend jFusion. It seems to be the most popular and well supported extension for doing what you're looking for. In the past, we've helped users overcome most, if not all, issues they've run into while trying to use jFusion... in honesty though, we haven't had a jFusion question in about 6 months, that I can remember.
In general though, JFBConnect creates 100% standard Joomla users, which should be able to be synced to other Joomla sites. However, please note:
1) This would sync just the Joomla user (their J! username and password), not necessarily their FB connect information for logging in that way on other sites.
2) You should be able to easily copy the FB/Joomla usermap stuff between sites, but jFusion (or others) likely won't do this automatically. It's a pretty easy SQL query to do so, and may be able to be inserted into a plugin for jFusion or something similar.
3) Even if the FB/Joomla usermapping information is copied, each site that Joomla is run on will need it's own FB app/secret key (if they're on different domains, at least). So, when the user first logs into a different site than the initial one they did, they'll need to approve the 'new' FB application. The logging in should be normal after that. This is not the case if the other Joomla sites are all in sub-directories or sub-domains of the original site.
Hope that helps explain. It will be complex, but it should all be do-able.
Alex