Q. Now hearts can be taken from completely dead donors; the donor heart does not have to be beating when it is harvested. How does this impact organ donation and Jewish law? I believe that one reason against organ donation is controversy surrounding whether brain dead is Halachikly dead. 
The following excerpt briefly explains the issue Two months ago, doctors in Australia transplanted a “dead heart” — a heart that had stopped beating inside a donor’s chest — into a 57-year-old woman. The operation, which has been deemed success, was unlike any other, because for the first time, it didn’t involve a brain-dead donor whose heart was still beating.
Normally, heart transplants call for the removal of a still-beating heart that’s put on ice for a few hours until it can be placed in a recipient. But two months ago, that didn’t happen. Doctors removed a heart that had stopped beating, and placed in a machine called a “heart-in-a-box.” That machine then revived the heart by pumping warm blood into it. “We removed blood from the donor to prime the machine,We then take the heart out, connect it to the machine, warm it up, and when we warm it up, the heart starts to beat.” Once the recipient was ready, the doctors disconnected the warm heart from the machine, and placed it in the patient. The technique effectively eliminates the current requirement for brain-dead patients. (from http://www.theverge.com/2014/10/24/7064353/doctors-transplanted-a-dead-heart-and-it-worked)
Is this transplant permitted in Halacha?

A. Horav Shlomo Miller’s Shlit’a opinion is that in principle it is permitted, if the patient has also stopped breathing and is truly dead. However, in practice as long as the patient can still be revived and his heart restarted, he is not considered death by the Halacha. The Rov commented that in today’s culture, when saving and extending the life of the terminally ill or the elderly is perceived as detrimental for them, the cost an unnecessary and unwanted burden on society and DNR policy rules, one has to be extremely careful to ascertain that before the heart is removed from the “death” patient, that he is indeed irreversibly dead, and cannot be possibly revived.

Rabbi A. Bartfeld as revised by Horav Shlomo miller Shlit’a.