To move from Joomla 2.5 to Joomla 3.x with JFBConnect, you'd want to:
1) Copy the following tables from your Joomla 2.5 site to your Joomla 3.x site:
#__jfbconnect_config
#__jfbconnect_channel (only in JFBConnect v6.0+)
#__jfbconnect_notification
#__jfbconnect_request
#__jfbconnect_user_map
#__opengraph_action
#__opengraph_object
#__opengraph_activity
#__opengraph_action_object
2) Install JFBConnect on the new site. Your tables and settings should be updated automatically.
That should be it. Of course, if you run into any issues, or have any questions, just let us know.
Not really understanding how this app works, I actually thought it would get the data from Facebook for the Likes and Comments that were previously done on the Joomla 2.5 site, but apparently that isn't the case.
JFBConnect won't 'migrate' your Likes/Comments. Those are all based on the URL that the Like/Comment were made on. There isn't a way to transfer them to a different URL. That's simply how Facebook works.
I'm assuming, since you've been using JFBConnect previously, you know our main features. We did just release
JFBConnect v6.0
with LinkedIn integration and other features.
I hope that helps explain,
Alex