Martin,
JFBConnect doesn't have any way to allow admin authentication. It's something we've considered, but haven't investigated in depth and there's no simple line or 2 of code that would allow it. It would take a substantial reworking of JFBConnect, and it's not something we have plans for anytime soon.
We recommend using the standard Joomla login for the admin area as it adds less complexity to the process and, generally, you should have a raw super admin account without extra stuff attached to it anyways.
I hope that helps,
Alex