Does one who donates his live sacrifice to a poor family receive the reward of the sacrifice?

If a man gives a sheep to a family for them to slaughter it as an Udhiyah (definition) (sacrifice) on his behalf and benefit from its meat, then this is a valid Udhiyah, and he will receive its reward. However, if he donates a live sheep to them and they slaughter it for themselves, then he receives the reward of charity (Sadaqah (definition)) but not the reward of Udhiyah. What he did is contrary to what is better, as Udhiyah is more virtuous than giving charity with its price. Furthermore, preferring others in acts of drawing closer to Allah (Qurbah) is not legislated according to the majority of scholars.