That's sad, Alice. The thing is, those parental declarations are the hardest to break. What needs to happen first with your friend is to have her experiences with her mother validated.
Maybe start by saying, "Gee, that must have been hard, and you probably felt like she didn't think you could do it, or that it wasn't worthwhile."
Later, after she has had time to digest that, you can maybe say, "Your mother was wrong. If playing the piano is something you truly want to do, you can. Have you thought about starting lessons now? It's never too late.