How to enable my web application to support facebook registration plugin

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Facebook-API

I have a web application in which i have two options by which user can log in to it-

General user (provided by common password),
Priority user(having username and password)).
Now what I want to do is suppose a priority user forgets his username and password than he can avail an option of logging with Facebook account username and password. But again a question is there that is when user logs in a web application how does Facebook authenticate that a user is General or Priority ?

Also my company don't allow user(priority) to register using an email.