Is it permissible to make a will to donate an organ, such as the heart or liver, and what are the evidences for this from the books of the Imams and the four schools of thought?

Bequesting organs for donation after death is permissible. As for donating them during life, there is a detailed explanation: If the organ is essential for life, it is not permissible to donate it. However, if life does not depend on it and no harm comes to the donor, then the majority of jurists and jurisprudential councils deem it permissible.