Question

As far as I know, the Facebook send dialog does not have any callback parameters (like the feed dialog). But, I would like to be able to store the recipients of that message in order to be able to control the access on it. Is that possible?

Answer 1

You can subscribe a call-back function via javascript on your page that has the send dialog
See: http://developers.facebook.com/docs/reference/plugins/send/ and http://developers.facebook.com/docs/reference/javascript/FB.Event.subscribe/

message.send – fired when the user sends a message using the send button. The response object passed into the callback function contains
the URL which was sent:

So according to the documentation you will only get the URL shared, so if you had multiple Send buttons on a page, you can tell which one was clicked.

For security and privacy reasons you cannot get the recipients of that message.