Organs cannot be transplanted if the person is dead.
Whenever an organ transplant takes place, it means the donor was still living (even if near death and unconscious)
Discussion
It also depends on the organs being taken. Bone, Skin and Heart Valves can be retrieved up to 24 hours after circulation has ceased and can be stored for months or years.
https://www.nhmrc.gov.au/sites/default/files/documents/reports/organ-tissue-after-death.pdf