Is it possible to authorize a Facebook user to send me a private message into my Inbox?

I definitely know that you can't send a message to other users, but is it possible to allow users to send messages to me?

Lik something similar to Twitter's direct messaging API, w开发者_如何转开发here the user authenticates my app to allow them to send messages through the app to me?

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No.

Sending a private message to a user using graph API is impossible at this time.

You CAN however use this (using Javascript SDK): http://developers.facebook.com/docs/reference/dialogs/send/