According to the late Ayatullah al-Khu’i, donating some of the organs (whether minor or major) after the death is permissible provided you have expressed your intention clearly in your will.

Ayatullah Nasir Makarim also holds the same opinion.

Ayatullah Khamenei allows this provided the body does not look like a mutilated body — so donating internal organs would be permissible but cutting off the external organs would amount to mutilation of the corpse which is not permissible.

However, Ayatullahs Sistani and Jawad Tabrizi do not recognize the validity of such a will at all; and, therefore, donating an organ after death is not permissible in their views