Question: Are we allowed to donate our organs upon our death? For example our heart, liver, kidneys? Is the soul still attached to the body once we are dead, or is that not true?
Answer: It is permissible, but it is not permissible, as a measure of precaution, to cut an organ of a dead Muslim if he bequeathed, unless a Muslim’s life is in danger. (http://www.sistani.org/english/qa/01277/)