Which statement is false?
organ rejection is a big risk in patients with organ transplants.
donor organs are treated with disinfectants and antibiotics before they are placed in the recipient.
anti-rejection drugs suppress the immune system, making the patient at risk for other illnesses.
it is not possible to contract an illness from an organ transplant.

Anti-rejection drugs suppress the immune system, making the patient at risk for other illnesses is a false statement.

Explanation:

Immuno-suppressive drugs provides support to the organ transplanted patient (recipient). Because it prevents their immune system in order to avoid the transplanted organ rejection. Recipient might also take this drugs for longer time which does not causes any illness to them.

Of course, rejection of transplanted organ makes the patient life into risk. Also, transplanting organ from donor to recipient is like replacing damaged organ and not curing of any illness. And, the organ should undergo treatment to screen infections.

i believe it would be the lungs.