Is it against Halacha to donate one’s organs after death? Is brain death considered death in Judaism?
The main problem with organ donation is that for major organs (heart, lungs, liver), there is a chance that the organ will be cropped while the donor is still halachically alive, implying his halachic murder. As the quesiton notes, one of the main questions is the determination of the moment of death, which is a question that has been widely debated by halachic aurhorities.
For this reason, many poskim object to organ donations on religious grounds. However, in the State of Israel the Rabbinate has become involved in the matter, and arranged for donations to be performed only after the halachic death of the donor has been verified (see the source quoted below). Not all rely on this arrangement, but many do. Another issue is the question of being buried with all one’s organs intact, which is important in the kabbalistic tradition, though this issue would not be weighty enough by comparison with the potential saving of a person’s live by means of the donation.