Is the recipient of a charitable donation rewarded for the value of the sacrificial animal?

The recipient of charity takes ownership of the alms through possession. Accordingly, the aforementioned sheep became your private property as soon as you took possession of it. You are free to dispose of it by slaughtering it or otherwise. If you slaughter it as an Udhiyah (sacrifice), you will, Insha' Allah (God willing), receive the reward for the Udhiyah. This applies if the donor gave you the sheep alive and did not appoint you as his agent for the sacrifice. However, if he gave it to you slaughtered, or appointed you to slaughter it on his behalf, then the Udhiyah is for him, and the meat is yours.