What is required of a person whom Muhammad and Hassan appointed to offer a sacrifice on their behalf, if he designated a sacrifice for each of them, then intended the first for Muhammad but mistakenly uttered it for Hassan, and when he realized his mistake, he designated the second for Muhammad both in intention and utterance?

If the agent intended the Udhiyah (definition) for Muhammad, but made a mistake in the utterance, then it is for Muhammad, because intention is what matters. If the agent slaughtered Hasan (definition)'s sheep for Muhammad, thinking that the first one was for Hasan, then it counts for Hasan, and the agent is excused for his mistake. The jurists have stipulated that if a person slaughters someone else's Udhiyah, believing it to be his own, it is sufficient for its owner. What another person slaughters by mistake on behalf of the owner of the Udhiyah is valid for him without compensation; they [the two parties] then exchange [the sacrificial animals]. No consideration is given to the error in specifying the two Udhiyahs, as each one has taken its rightful place and sufficed for its owner.