If I am awarded guardianship of my incapacitated mom in NY, can I move her to where I live now in Oklahoma?

Should you be awarded guardianship/conservatorship over your mother and her estate, you can ask the court to be allowed to transfer jurisdiction to your home state. Once you have been appointed guardian/conservator, be prepared to explain/show to the court how this will be in your mother's best interest. If the court agrees, you and the courts in both OK and NY will work to change jurisdiction.

Not yet. Her guardian is a long-term live-in boyfriend. He has been neglecting her for years.. now there is a hearing. He may lose it and I am only child of hers that will do it. If I am awarded I want to move her here. No family lives in NY.

Have you actually been awarded guardianship by NYS?
Mom is legal resident of NYS?
Or is more theoretical & is there other family in NY?