let’s start with the easy part, and that’s the extra 15 lbs. Chances are that it was not only the lack of ‘formal’ exercise that caused the weight gain but a combination of more calories and less incidental activity. As we are only talking about 15 lbs, a mindful eye on a healthier diet should gradually help the client to get rid of the extra weight.
As far as the full recovery is concerned, please keep in mind that your client is only about 4 months post-op. Whether that constitutes a long time or not depends a lot on what kind of knee surgery your client had. I have often observed that surgeons tend to be overly optimistic in their prognostication about recovery time. Clients often told me that they were supposed to be back to work the next week and then are disappointed when that is far from the reality. Even with PT, I have observed that clients get little help with the secondary consequences of surgeries such as back and hip problems as a result of altered gait.
I would certainly start with the T exercises and gradually built from there but would also immediately start with anything that strengthens hip and core to prevent problems in that area. If your client has access to a pool, then activities such as water walking in all directions can assist with recovery. Swimming can help get started on a more vigorous cardio program as long as it is not breast stroke.
Good luck for you and your client.