All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.
Firstly, organ donation is permissible provided that certain conditions are met, as has been explained in fatwa 86647. It is also allowable to transplant an organ from a dead person to a living person provided that certain conditions are met. We have also underlined that there is no religious impediment to transplanting an organ between a Muslim and a non-Muslim provided that the due conditions of organ transplantation are met, as has been explained in fataawa 197739 and 84542.
As for organ exchange, there is no harm in it as long as it is a donation, but if it involves stipulated conditions, then it appears - and Allaah knows best - that it resembles selling, and the selling of organs is forbidden according to the resolution of the Islamic Fiqh Council, which says, “It is impermissible to subject human organs to sale under any circumstances. As for the beneficiary spending money in order to obtain the required organ where necessary or offering a reward to the donor or honoring him, this is subject to ijtihaad (juristic reasoning) and further discussion.” Hence, organ exchange (which you mentioned) should not be opted for except in case of necessity.
It is permissible to transplant an organ from a dead person to a living person whose life depends on receiving that organ or whose vital functions would otherwise be impaired on the condition that permission is given either by the person before his death or by his heirs after his death or by the Muslim ruler or leader in cases where the dead person’s identity is unknown or has no heirs. For more benefit, please refer to fataawa 84780 and 81180.
Allaah knows best.