From the "Connect with their Facebook logins" aspect, that's pretty much 99% of what JFBConnect does. Can you explain "control who is able to log in" more?
We currently don't have a way to manually create a connection (we call it a user-mapping) between a Facebook user and a Joomla user. However, adding a "New" button to the usermap admin page would be trivial. Basically, it would be pretty easy to set your Joomla site up like:
* Turn off user registration
* For each user you want to be able to log in, create them a Joomla account
* Create a new usermap field in the JFBConnect administration area where you input their Joomla ID and Facebook User ID (You'd need to get this from them).
Another alternative that we're working on that may work for you is an automatic mapping of a Facebook user to a Joomla user. In this case, if a Facebook user logs into your site for the first time, IF their Facebook address is the same as a Joomla account already on your site, we'll create the connection between the 2 automatically. Currently, we throw an error because it looks as though someone's trying to register with the same email address as another user. By using this method, your client could create an account for your users and then disable user registration. If he never distributes their passwords to the users, but instead tells them to log in via Facebook, this will automatically connect their accounts and prevent them from logging in from Joomla... you'd need to hide the Joomla user details screen and other things to prevent them from updating their password, so this isn't a 100% solution, but close to what I think you're looking for.
The above request for automatic mapping is from a request from a current subscriber. We prioritize all subscriber requests, so if you choose to do so, you know you'll have the help you need to get up and running!