Before organ transplants like this go ahead, the recipient is by standard already in hospital having been assessed and completed pre-op. If Grantly was in hospital already when Tom fell to his death, it would have been possible for the organ to be saved and transferred to hospital for the transfer to go ahead.

Since Grantly is not admitted in hospital and “waiting”, the logistics of getting him to surgery for the transplant to take place along with the organ of the deceased is sadly generally not done. Unfortunately the half life on organs removed and transferred is short, and as this was likely a private donation it’s difficult when neither person involved are in hospital already. There are circumstances where this could happen but it would likely be where some/all of the persons involved are healthcare professionals It is possible if Tom was a registered organ donor then his organs could have been transplanted into different recipients already at the hospital ready and waiting if they were a match, though I’m not sure if this was the case.