I also suffer from severe cases of fibromyalgia we've tried different treatments the only thing that helps me lessen the pain is narcotic pain management and Lyrica we tried the Cymbalta but that didn't help much. I have some exercises I can do with the big ball and when I can handle it I go to aqua water classes. Problem with treatment options is it depends on each individual problem there is no one answer to the question.
I wouldn't suggest any one particular exercise it all depends on what your body can handle, some days I'm great and can go out and walk around my neighborhood. Other days the pain is so severe I can barely make it from the bed to the bathroom. Like most exercise facilities will tell you always get your doctor's permission to start classes or training. I like crafty have a lot of pain at night with muscle tremors and shakes so again it's to meds to sleep.
Best thing for your sister is to see a doctor and get a referral to a pain management specialist.