I am conscious that Facebook Designers provide a wordpress plugin for websites that enables customers to comments with an article via their Facebook account.
However, my real question is whether comments from the Facebook page could be moved instantly to some website. For instance: for any Facebook page owned by a newspaper, when articles is released around the the wall from the newspaper's Facebook page, so when people comment or "like" it, can these comments and likes be moved instantly towards the article around the newspaper's website that's fully integrated using the wordpress plugin. Or are comments with an article published around the Facebook page wall different and incompatible with comments with an article published around the website's page?
You'll have to programmatically make use of the Facebook Graph API to retrieve your comments ought to left in your Facebook page posts, then render these in your corresponding articles in your Site.
The Facebook Comment plugin loads comments associated with specific Web addresses (e.g., yoursite.com/article/123). Facebook won't relate those to specific posts in your Wall for you personally.