This would be a great assignment! You have a good teacher. The letter that Rahim Khan delivers to Amir is to be found in Chapter Seventeen of this amazing novel. In this letter, Hassan makes it clear to Amir how the take over of Afghanistan by the Taliban has impacted Hassan and how what has happened in the past likewise affects his dreams. However, throughout all of this, his unchanging loyalty and love to Amir is established and confirmed as he wishes that Amir would return to his homeland and see his friend.
One of the crucial aspects of the novel is that Amir tries to forget what happened with Hassan and lock it away. However, he finds that it is not so easy to put away such dangerous and painful memories that are the subject of such guilt. My first thoughts in responding to this question would be that what has happened between them is too big a matter to talk about in a letter - I would rather do it face to face. Yet, if you had to write a letter, I would start by talking about Amir's life in the United States and his wife before moving on to the real unspoken topic that must be dealt with - Amir's treatment of Hassan when they were children - his reluctance to help him while Assef raped him and then how he "organised" for Hassan to leave.