For Muslims to be allowed or not allowed something, one must first understand the reasons under which a ruling is given. For something that was not an issue at the time of the Prophet (pbuh), scholars today have to get together and give a joint fatwa/ruling over the issue at hand. In the case of organ donation majority scholars did give a ruling that since Islam is a religion that promotes the well-being of human beings and scientific advancements that go on to do that are encouraged, organ donation from a living person or from a dead person is allowed as long as the living person is not harmed, the benefits outweigh harm, there is no ‘sale’ of organ donations and that it is indeed providing a healthier life to someone at risk. I hope this answers your question and for anything in depth I suggest you go to your local scholar.
