The right answer is transplant (or graft).
In medicine, a transplant is a surgical procedure that consists of replacing a diseased organ with a healthy organ called a "graft" or "transplant" from a donor. The difference between these two term is that the first is performed with a surgical anastomosis of the feeder and / or functional blood vessels, while the second is avascular.
The organs (usually) are therefore transplanted: heart, lung, liver, kidneys, while the transplants concern the cornea, the cord, and so on.
