So I started to get a little curios about this, so I went to the Halachic organ people’s website.
So they have a video of Rav Dovid Feinstien which they label as him “encouraging” organ donation. So if you watch the video, you see that he says not to. He says that if there is a person in front of you who will get the heart, and the patient is “dead” which he defines as no longer breathing, then you should give it. But that you shouldn’t put the heart into the organ pool.