[The following is a translation of the Shaykh’s answer.]
Question:
Your Excellency, Shaykh, may Allah bless you. We ask for a clarification of the legal ruling concerning organ donation in cases of life, death, or brain death.
Shaykh Abdullah al-Mutlaq:
Organ donation is a blessing among the blessings that Allah Almighty has bestowed upon people in this era (‘Asr). How many people would otherwise remain in constant suffering, continuing, for example, with kidney dialysis, whereas modern science has now made it possible for them to benefit from organ donation.
If we were to say that this is impermissible, we would deprive many people of donations made to their fathers, mothers, siblings, and relatives, and thus we would lose something immensely valuable. Allah Almighty has made organ donation one of the means of preserving life. Allah the Exalted has said: “And whoever saves one life, it is as though he has saved all of mankind.”
(First) As for organ donation from the living, this is now practiced, accepted by people, and has become something embraced throughout the world, especially with regard to organs such as the kidneys. Kidney donation is now widely known, and many people have received donations from their sons, wives, husbands, or others. Thus the blessing is fulfilled, relief is attained, and the sick person regains full health. This is a great blessing.
Second, there is donation after death, whether initiated by the donor himself—by registering a card stating, “I am a donor”; indeed, I myself have such a card indicating that I am donating my organs after death, and I am among those who hold this view and strongly support it—or through the authorization of his relatives to donate his organs.
We should not forget that some of our scholars—may Allah gather us and them in Paradise—used to prohibit this very strongly. However, the truth is that with the advancement of science and people’s recognition of this great benefit… I am speaking, for example, of a woman who died at the Specialist Hospital. Two kidneys were benefited from, as well as, for instance, a pancreas and a heart; they transplanted her heart, and I believe also a lung. How many people can benefit from this?
Some people say: “No, this is mutilation.” But where is the mutilation? The woman’s body remains intact; these organs are taken from within the abdomen, and nothing outwardly visible is affected. That is the first point.
The second point is that one is faced with two possibilities: either one takes this organ and transfers it to a body in which it is preserved and through which life is sustained, allowing acts of worship to continue for a long time, or one leaves it to be consumed by worms. Indeed, in less than a week, it is over: it is eaten by worms and no benefit is derived from it.
Whereas this, my brother, is an ongoing charity (Waqf). When Allah grants renewed life filled with well-being through a few organs—two kidneys, a lung and a heart, or two lungs and a heart—how many people will recover health and bodily well-being through such things, without any harm coming to the deceased? Your companion is dead—dead, finished, gone. His soul has departed, InshaAllah, to Paradise and to goodness, while as for his body, it is buried and will return to dust.
As the Prophet, peace and blessings be upon him, said, “The son of Adam will entirely decay except for the tailbone,” that seed from which he was created and from which he will be reconstituted on the Day of Resurrection. As for the rest, it perishes.
Therefore, my dear ones, we say that organ donation is a blessing. It has been permitted by the fiqh academies and by many fatwa institutions, including Dar al-Ifta’ in Egypt and others. This practice continues in the hospitals of Islamic countries today; it is ongoing among people in this manner, and Allah has brought about through it immense benefit.
[End of the Shaykh’s answer.]

About Shaykh Abdullah al-Mutlaq:
Shaykh Dr. Abdullah ibn Muhammad al-Mutlaq (Hafidhahullah, born in 1374 AH (1953 CE), in al-Kharfa, al-Aflaj Governorate, Saudi Arabia) is one of the senior contemporary scholars of the Kingdom of Saudi Arabia. He serves as an Adviser to the Royal Court and is a member of the Council of Senior Scholars, the Kingdom’s highest official body of religious scholarship. He is also a former member of the Permanent Committee for Scholarly Research and Iftā’, and he has headed the Department of Comparative Jurisprudence at the Higher Institute of the Judiciary, affiliated with Imam Muhammad ibn Saud Islamic University, from which he earned his PhD in Comparative Jurisprudence. Widely respected for his juristic learning, teaching, authorship, and public guidance, Shaykh al-Mutlaq occupies a distinguished rank among the Saudi ʿulamāʾ and is recognized as a leading authority in fiqh and fatwa. (Summarized from Saudipedia.com)
(Translated by Mohammed bin Thajammul Hussain Manna.)