My mom's friend talked her into starting a janitorial business last year. She is 74 yrs old and has Alzheimers. (Not severe enough to be declared incompetent) She got a fictitious business name and gave her friend approx 20k to get the business off the ground. Mom got sick and was hospitalized for several months. Surprise, surprise, the business never got off the ground. Can she write any of the 20k off on her taxes? Does she need to file taxes? She refuses to believe that her friend scammed her. Any suggestions? Maybe I should be posting this under elser abuse?

Business losses require some income first (a few rare exceptions) to prove that it is really a business, which this isn't, unless the partner/friend can come up with some paperwork showing the business got off the ground.
You may have a tough time with elder abuse because she got sick, but she could sue for her money back anyway (she may or may not win). It's way over the Small Claims limit so she would have to either sue in regular civil court, or reduce her damages to the small claims limit in her state.

Perhaps it's time for you to get power of attorney with your mother's blessing, just with the promise that you want to help her hang onto her money.