Hi, it is possible to keep comments when you move pages; the unique id facebook uses to access comments for a particular page is the page's URL, however when you place a comment box on a page the specified URL does NOT need to be the url of that page - eg it is possible to have multiple comment boxes on a single pages displaying comments from different sources.
Nevertheless, facebook used to restrict this by requiring that the comments comes from the SAME domain, or the domain of the Facebook application, etc. - I haven't tried whether or not some domain restriction is currently in place. Assuming there isn't one, you can add comments to a post by simply disabling (automatic) comments for that post - http://wp-connect.tomasvorobjov.com/docs/#plugins-position
- set comments to "enabled"
- set the position to "custom"
- use the toolbar to generate the comments shortcode
[wp_connect_comments href="http://dezertdezinez.com/igwt2/?p=332" colorscheme="dark" num_posts="10" width="400" /]
Please let me know if you need any additional help