Usually a person recovers after knee replacement almost fully but that is also dependent on factors like pre existing strength of the knee muscles and prior active life.  The quadriceps muscle may get weak after surgery which should be prevented by exercises. If  it's weak then your quadriceps muscles aren't strong enough to lift your mother's own body weight. It needs to be strengthened with an extra punch.

Hi , how long is it since her surgery got over? If you are training her for the first time for stair climbing remember a simple technique ...while climbing up good leg(non operated leg)should go first, while defending stairs...operated leg should come first..... Remember the logic Good leg goes to heaven(climbing up) and bad leg goes to hell.(climbing down) 😃