Patient 1 and patient 2 both had a transplant. which explains why patient 1 had a successful transplant and patient 2 did not?

There are many factors that might affect the failure of Patient 2's transplant operation. It could be 'transplant rejection'.

The process when a transplant recipient's immune system attacked the transplanted organ or tissue is called transplant rejection. This is the common cause why some transplant operation fails. Our immune system protects our body from harmful substances that might be present in the transplanted organ.

No they’ve not done that