What is obligation to family who donates organ of loved one?

Donor family. A Decision to donate organs is up to the deceased (if they signed up to be an organ donor) or to the next-of-kin (if the deceased is not an registered organ donor). We (the society) all owe the donor families a great deal of gratitude and the best way for organ recipients to "pay" them back is by taking care of the donated organs.
To be PROUD. You have done a wonderful thing. Your loved one will live on both in the health of the recipient, and by the memory of your wisdom at a time of crisis. Thank you on behalf of the human race.