All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
Sharing the price of a sheep for udh-hiyah by more than one person is invalid. As far as we know, the scholars unanimously agree on this. However, sharing a camel or cow is valid, according to the majority of scholars. The Maliki scholars are of the opinion that it is invalid. But the opinion of the majority of scholars is the preponderant. This is based on the hadith that was narrated on the authority of Jaabir who said: "When we were in the company of the Messenger of Allah, sallallaahu ‘alayhi wa sallam, in the year of Al-Hudaybiyah, we slaughtered a camel to be shared by seven persons and a cow to be shared by seven persons. " [Muslim]
The hadith talks about hady (Hajj sacrificial animal), but the same ruling applies to udh-hiyah.
Consequently, if that person paid a part of the price of a sheep, it does not count as offering a sacrifice on his part. But if it was a part of the price of a camel or cow, it is counts as such, by the permission of Allah.
We underline that a person who is able to offer a sheep can let others share with him in the intention of offering it as udh-hiyah but without paying part of the price. It was narrated on the authority of ‘Ataa’ ibn Yasaar that he said:
I asked Abu Ayyoob Al-Ansaari, about the manner in which they used to offer udh-hiyah during the lifetime of the Messenger of Allah, sallallaahu ‘alayhi wa sallam, and he said, "A man would sacrifice a sheep on behalf of himself and his household, and they would eat some and give some to others, until people started to do it out of boastfulness and it became as you see now..." [At-Tirmithi and Ibn Maajah; saheeh]
It was narrated that a ram was brought to the Prophet, sallallaahu ‘alayhi wa sallam, and he slaughtered it with his own hand. He, sallallaahu ‘alayhi wa sallam, said: "Bismillaah, wa Allahu akbar (In the Name of Allah, Allah is Most Great). This is on behalf of myself and on behalf of those of my Ummah who have not offered the udh-hiyah." [Ahmad and Abu Daawood]
Allah Knows best.