Finn,
Thanks for your PM with details about your site. I just tried to access your site, but the Joomla admin credentials weren't working.
However, I re-read your message, and I think I understand where the confusion is coming from. The "This extension does not appear to be installed." message on the JFBConnect Overview page is not talking about the 3rd party extension that JFBConnect integrates with, it's talking about our plugin that is meant to do the actual integration. In the
My Subscriptions
area of this site, there are extra files to download, in addition to the main component. Mainly, get the jfbconnect_profile_plugin zip file, unzip it, and install the profile plugin for JomSocial. Once installed, you should be able to configure the integration in the "Profiles" integration tab.
Hopefully, that's the whole problem, but if not, just let us know!
Thanks,
Alex