Is the sacrifice slaughtered by the father on the first day of Eid sufficient, considering that the son intended to slaughter it on the second day?

If a Muslim designates a sheep for sacrifice (udhiyah) and someone else slaughters it without his permission, the sacrifice is valid and sufficient as long as it is within the time of slaughter. The one who slaughtered it is considered a deputy for its owner, as customary permission is valid even if not verbal. The rules of Sharia have established that customary permission is like verbal permission, and deputization in udhiyah is valid from a Muslim, and there is no liability on the one who slaughtered it.