Is a patient suffering from brain hemorrhage and hemiplegia obligated to make up the prayers she missed during her treatment in the hospital or after her discharge, or is she exempt from making them up?

Your sister must pray as long as she is conscious. She should pray according to her ability. If she cannot perform ablution, she should perform tayammum. If she cannot stand, she should pray sitting or lying down. If she is only able to articulate the prayer in her heart or with a gesture of her eye, that is obligatory upon her. She must make up for the prayers she missed due to illness, and she is permitted to delay making them up until she recovers.