The Bible doesn’t give any direct information about this issue (because organ doning is a modern medical procedure), so we have to look at the principles it presents and try to best apply them in this situation.
A basic Biblical principle that we might take into consideration is that Christians are called to be loving to others (Lev. 19:18; Mat. 5:43; 19:19; 22:39; Mark 12:31; Luke 10:27; Rom. 13:9; Gal. 5:14; James 2:8), especially those in need (James 2:15-16; 1John 3:17): providing an organ for someone who is in need of a new one is a very loving thing to do.