@jeeeemv, I'm going to go along with the doctor's opinion that this dizziness will go away in time. Recovery from transplant surgery is an individual thing. So much depends on the patient's pre transplant conditions and any pre existing health conditions.
Using a walker and a cane is great! It is a proactive way to assure that client will get up and moving. This will help increase strength and stamina for independence. I needed physical therapy because I had been depended on a wheelchair and walker prior to transplant, due to my advancing liver and kidney failure. Healthy eating, staying hydrated, and getting physical activity like walking are what my team advocated for me. As a patient, and that is what helped me. Take it slow and steady with slight increases. Also make sure that patient IS taking medications according to the doctor's orders. There will be some adjustments as time passes, but for now - the health of the new kidney and preventing rejection if the primary concern.

jeeeemv, Has your client thought about keeping a list of when he/she notices the dizziness? This might be something for the transplant doctor to see. Is there someone who is available to be with client when he does walk?