I have trained a client with similar limitations, even though it was her right side that was weaker. I started training her when she was 80 years old.
I did as many unilateral exercises as possible to try to bring the weaker side ‘up to speed’ to the degree possible. I also worked on balance using equipment such as balls (as in wall squats), balance boards and dyna discs. I also included some playful exercises such as catching a ball to improve hand/eye coordination.
With my client, we made quite good progress for a number of years. After a while, it was a matter of maintaining what we had, and then I gradually needed to yield to the realities of her getting older. I trained her for 10 years; she then suffered another stroke and had to go to a nursing home where I was not allowed to train her.
If you train your client for that length of time, be prepared for a decline that you can only delay but not prevent. It can be emotionally quite difficult.