Facebook API does not provide any method for sending a message to the inbox of a user. Fortunately, messages can also be sent using XMPP, which is used by facebook chat, but can also be used for sending a message to a user that is offline (i.e., the message will appear in the user's inbox).
In this link you can find a php class that utilizes facebook's XMPP functionality and sends a message to a facebook user.
In order to use this class you need to obtain an API key, by registering your application here. In order to use this class you should provide, your API key, your user id, the current authorization token, and the user id of the user to which you wish to send a message.
In order to get your user id, you can user the facebook php sdk and use the getUser() method of the Facebook class. In order to get the authorization token you can invoke the getAccessToken() of the Facebook class
In this link you can find a php class that utilizes facebook's XMPP functionality and sends a message to a facebook user.
In order to use this class you need to obtain an API key, by registering your application here. In order to use this class you should provide, your API key, your user id, the current authorization token, and the user id of the user to which you wish to send a message.
In order to get your user id, you can user the facebook php sdk and use the getUser() method of the Facebook class. In order to get the authorization token you can invoke the getAccessToken() of the Facebook class
