JFBConnect v6 has a Joomla 2.5/3.x compatible installer, which should work for both versions of Joomla. JLinked, when it was discontinued, still required separate installers for both.
With that said (even if it's technical mumbo-jumbo), what I'd recommend doing is:
* Backup!
* Install JFBConnect v6 on your Joomla 2.5 site.
* In the Configuration -> LinkedIn area, go through the migration steps for copying your settings, deleting your tables and uninstalling JLinked
At that point, you should be able to upgrade Joomla 2.5 -> 3.x. It won't hurt if you re-install JFBConnect again on the new site. The main things are that the database tables copy over when you do the upgrade or migration, depending on how you're actually moving to Joomla 3.x.
I hope that helps explain, but if you have any questions or run into any issues, just let us know.
If you liked JLinked.. I think you're going to love JFBConnect

There's a lot that's been improved in that over JLinked and the 6.1 release, due out in June, will simply continue to make it better
Best of luck, and keep us posted on how things go.
Thanks,
Alex