Source: Shiloh Musings
Recently Avi Cohen, an internationally known Israeli soccer player, died as a result of an accident. Years before he had signed instructions that his usable organs should be donated to save other lives. For some reason, this didn't happen.
I personally know people who are alive today because there are healthy organs in their body from others, and I know some of the people in this very powerful and moving HOD movie.
I'm not an expert in Halacha, Jewish Law, so my reasoning is based on my logic. If it's permitted to receive organs, then it must be required to donate to others. This way more lives will be saved, a very great mitzvah.