Add feature sponsor my facebook friends to website

Currently, we use a simple form with four fields : firstname, lastname, email, invitation text (see image 1). On submit, our application populates a table (see image 3) and generates a unique id which is present in an url sent within the email message (see image 4) to the invited friend. When he clicks on the link, we are able to track who originlly sent the email. Basic tracking which works fine. With the Facebook buzz, we need a way to allow our members, who have a facebook account, to easily invite their facebook friends to become members of our website instead of filling our current invitation form. When a friend register, we need to know who invited him/her, so basically we need the same process.