We have to move Mom (early stages Alzheimers) from Memory Care in SC to Memory Care in FL - what do we tell her?

You do not tell her anything. She will not be able to process any detailed explanation about why the move is necessary. Is she going to be closer to family members? Is she in a locked facility now? Take her on an outing move day. Have her room already setup when she arrives. Do not wait until she is there to do the arranging and such. That will be very hard for her.

As long as the room looks the same, with some of her personal items, she won't know there is a difference. Just ask her how she feels and encourage her to have a nice day.