JFBConnect can't do this automatically for you. It's a pain when your URL structure changes both for SEO and social sharing purposes.
All social sharing features are attributed to one unique URL. If that URL changes, there's no way to transfer the social stats. You can only continue to use that old link along with the new page as described below. It can get tedious to manage. What we usually recommend is picking 5-10 pages that are critical based on their comments, sharing and other factors and only try to keep those social stats. The rest, just let them reset.
With that said, to make old Like counts and Comments transfer to a new URL you need to:
* Keep the Like and Comment buttons pointing at the old link. To do this, you can't use the JFBC Content plugin to automatically add the social features. You'll need to use our configuration area to disable the automatic adding of those features to the articles or categories you want to save.
* In those articles, you'll need to add your own sharing buttons using our Easy Tags or the JFBCSocialShare module. Either method, you'll need to specify the old URL that the original sharing or comments were used on. For the EasyTags, you'll use something like:
{SCFacebookLike href=http://yourdomain.com/old-url-with-shares}
With that, the Like button will still tell Facebook to load the Like button for the old page and show it's comments.
Once that's all done, all you need to do is setup proper 301 redirects from your old content to your new content. That's important anyways for SEO purposes.
I hope that helps get you started, but if you need anything else, just let us know.
Thanks,
Alex