I don't believe a letter will hurt. I don't know that it will help her long-term, if she has a problem letting go.....but you can try. I don't suggest you ask her for a written apology in return. I believe it would go badly. Hopefully, if the A has truly ended, and if she has him out of her head.....your written apology will be a step in her healing. Some day, hopefully, she will apologize for the A. Right now, her anger is preventing it.

A couple of positives in her receiving a letter is (1)she can't interrupt it to spew on it, and (2) she can keep it to read over as many times as she feels the need. Oh, and another...she may read something she didn't hear in the verbal apology. I can understand how her angry mind could run ahead of the words being said to her at the moment, and could actually prevent her from completely hearing everything correctly. Maybe she will be able to "hear" this letter with her heart. I hope she can.

It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!