Backing up is usually not too difficult to train. I've backed (broken in) two of my horses, raising one of them from foalhood. The way I did it (I don't know if it's the best way or even a good way but it worked!) was to stand in front of the horse and put one hand on her nose, then push back gently, saying, "Back" in a firm voice. I pushed harder and harder, pressing her nose towards her chest, until she took a step back. I immediately stopped pushing and praised her. Once she had the hang of that I took hold of the lead rope, still standing in front of her, and pushed it towards her neck, saying, "Back" and looking into her eyes. The moment she stepped back, I once again released the pressure and praised her, also looking away from her eyes. Once she was backing up beautifully on the ground, hardly needing the pressure on the halter and moving back at the word "Back", I got on her and gently rocked the bit by "playing" with my hands and pulling the reins slightly, saying, "Back, back". She stepped back and I released the pressure and patted her. If this doesn't work, have a friend stand in front of the horse and while you play with the reins and say "back", the friend puts their hand on the horse's nose and pushes her back, just like you did on the ground. It takes some time but is usually pretty minor. Hope this helps! I think it's great that you're helping your friend with her horse - training is such a rewarding thing. If this doesn't work ask a professional! And always remember to keep yourself and your horse safe.
