Your friend can go to the police. If your friend is willing to testify of abuse she has received and witnessed, it doesn't matter WHAT the mom thinks - the police will arrest the guy based on your friend's testimony.
Also she needs to go to the hospital if he ever hurts her physically, that way there will be documentation of injuries. She doesn't need her mother to go in and say "my mom's boyfriend/husband/my dad hit me and this is what happened." That's a fast way to get attention.
Sounds like its up to you to save her. I mean you need to convince her its ok to tell somebody. If she won't agree then you need to be her voice in this. Sometimes the abused are just too terrified to save themselves. If you know any of het family you can talk to that would be what I'd try 1st. Just tell somebody fast because should the abuse get worse and more permanent damage done you will feel guilty forever.