If the guy is really that emotionally attatched to her. He would let himself believe there is a chance to get back together, and whatever other people do or say won't matter to him. So, even if you send that letter, I would assume that he would just tell you, it is non of your business and continue bother your sister. The only thing that can help is time, this is coming from personal experience.

As time goes by, the guy should cool off and forget about your sister. For me it took about a year, and my case is more like phycial attatach rather than emotional.