Organ transplant

I wonder if it is possible to transplant female reproductive organs into a trans-sexual male? Or visa-versa? Could the sensitive skins of the original sex organs be kept, while the actual functioning reproductive organs be transplanted from a willing donor or deceased person? Transplanted is not the right word, as the organ is not being replaced with the same organ. However, if it could successfully be done, they could function reproductively as the new sex, so they could fully express the "woman" or "man" in their sexual functions and relationships. The once male could be a woman, mate, menstruate, and give birth naturally.

I have just been told by a trans-sexual that the donated organ would atrophy because the body of the recipient hasn't got the appropriate nerves to communicate what to do to the organ. So. due to lack of activity it would atrophy and basically rot.