There's a few options here, but it ultimately depends on where the data is being stored. JFBConnect relies on other extensions for managing profile data besides making the actual link to the social network for the user.
With that said, if you're using one of the 3rd party extensions where JFBConnect can send the user through the other registration forms (Joomla, JomSocial or EasySocial), you can use those registration flows with JFBConnect and use whatever fields you already have configured and they should just work. If you're using the JFBConnect Login / Register page, then you may need to add some custom code to make the field work and possibly some extra code to store the field properly.
So, can you give more information on the field you're saving, where it's going, and how it works for users that are registering normally through Joomla? That will help us provide the best answer for you.
Thanks,
Melissa