There is definite evidence for Christian support of organ donation.

The Lord demonstrated with his own life how, even in sorrow, love enables us to embrace the needs of others. We can choose to donate our organs to save the lives of many people. The decision to donate at the end of life is the beginning of healing for many others.
Healing and saving life is a great gift. Jesus sent his 12 disciples out with the imperative to heal disease and illness: “Heal the sick…freely ye have received, freely give.” (Matthew 10:8)