My best friend stole something. I thought it was wrong, so I confronted her and said that if she didn't return it, I would tell. I told, and the place said they couldn't do anything about it since I was just an anonymous source, and they didn't have real, solid proof. In the process, I lost my best friend because she said although she knows what she did was wrong, it wasn't MY place to fix it. It's not my job to be the savior in every single situation.
I agree with you that you can't sit back and just watch this stuff happen. But, I also agree with others that it's not necessarily your responsibility to take her down.
I tried to do the right thing, and the right thing never happened. Sure, i'm glad I told, but I lost my friend, and they never got their stuff back.
Talk to your friend... even though she submitted. Confront her. Even though she did something wrong, you are stooping down to her level by going behind her back. DO NOT write the letters. You won't feel better. I promise.