Hi, sorry to hear your sister has been having problems with a fake account. I recently had a couple of facebook accounts created in my name a couple of years back, and only found out about them because one tried to "friend" me and sent a rude message to my mother! All I did was report it to facebook, and got a few of my friends to report it too (I think the more people report something, the more facebook will take it seriously - stupid, I know!) Other than that, I'm afraid there's not much she can do other than tell people it isn't her making the accounts.
Unfortunately the internet, especially social networkin sites such as facebook, create opportunity for anonymous bullying from people who perhaps would be too cowardice to do it in real life.
Someone keeps opening accounts on things like fb (and a few other similar things) in my sisters name and saying horrid things to people who go to her school. Now other people are hitting her as a result of the horrid things said on fake fb account. My mum spoke to the police but they wont do anything and the school are investigating but as fast as the accounrs are being deleted more pop up.