Offering Udhiyah on Behalf of the Prophet
Question

Is it valid for a Muslim to offer an Udhiyah on behalf of the Prophet (blessings and peace of Allah be upon him)? What is the scholars’ view on this matter?
How sound is this Hadith and how is it to be understood? It was narrated from Hanash from `Ali (may Allah be pleased with him) that he used to offer an Udhiyah of two rams, one on behalf of the Prophet (blessings and peace of Allah be upon him) and the other on his own behalf. He was asked about that, and he said: He instructed me to do that – meaning the Prophet (blessings and peace of Allah be upon him) and I shall never stop doing it. Narrated by At-Tirmidhi and Abu Dawud.
Praise be to Allah.Can we offer Udhiyah on behalf of the Prophet?
It is not permissible for anyone to offer an Udhiyah on behalf of the Prophet (blessings and peace of Allah be upon him), because the basic principle with regard to acts of worship is that they are not allowed and should not be done unless there is proven evidence to the contrary.
Degree of the Hadith about offering Udhiyah on behalf of the Prophet
With regard to the Hadith referred to by the questioner, it was narrated by At-Tirmidhi and classed as inauthentic by Shaykh Al-Albani and others, as stated below.

At-Tirmidhi (1495) said: “Muhammad ibn `Ubayd Al-Muharibi Al-Kufi told us: Sharik told us, from Abu Al-Hasna’, from Al-Hakam, from Hanash, from `Ali, that he used to offer an Udhiyah of two rams, one of behalf of the Prophet (blessings and peace of Allah be upon him) and the other on his own behalf. He was asked about that, and he said: He commanded me to do that – meaning the Prophet (blessings and peace of Allah be upon him) and I shall never stop doing it. Then immediately after narrating the Hadith, he (At-Tirmidhi) said: We only know this Hadith from the Sharik.
It was also narrated by Ahmad (1219) and Abu Dawud (2790) via Sharik ibn `Abdullah Al-Qadi, with the word “instructed me” (this word is used to refer to instructions left by a dying person to be carried out after his death): `Uthman ibn Abu Shaybah told us: Sharik told us, from Abu Al-Hasna’, from Al-Hakam, from Hanash who said: I saw `Ali offer an Udhiyah of two rams. I said to him: What is this? He said: The Messenger of Allah (blessings and peace of Allah be upon him) instructed me to offer an Udhiyah on his behalf, so I offer an Udhiyah on his behalf.

Al-Mubarakfuri (may Allah have mercy on him) said:
“Al-Mundhiri said: Hanash is Abu Al-Mu`tamir Al-Kinani As-San`ani. More than one scholar criticised him. Ibn Hibban Al-Basti said: He made a lot of mistakes when narrating reports, and was the only one to narrate from `Ali things the like of which are not seen in the Hadiths of trustworthy narrators, to the extent that he became one of those who cannot be quoted as evidence.
Sharik is ibn `Abdullah Al-Qadi, concerning whom there are some reservations. Muslim narrated some reports from him in Al-Mutaba`at. (End quote)
I say: Abu Al-Hasna’, the Shaykh of `Abdullah, is unknown, as is well known. Therefore the Hadith is inauthentic.” (End quote from Tuhfat Al-Ahwadhi)
Shaykh Al-Albani (may Allah have mercy on him) said: I say: Its chain of narration is weak because of the poor memory of Sharik – who is ibn `Abdullah Al-Qadi.
Hanash is ibn Al-Mu`tamir As-San`ani, who was classed as inauthentic by the majority of scholars.
And Abu Al-Hasna’ is unknown.” (End quote from Da`if Abu Dawud)
It was also classed as inauthentic by Shaykh `Abd Al-Muhsin Al-`Abbad (may Allah preserve him), as it says in his commentary on Sunan Abu Dawud, for the reasons mentioned above.
Once it is determined that a Hadith is inauthentic, we must act on the basis of the general principle, which is that it is not permissible to offer an Udhiyah on behalf of the Prophet (blessings and peace of Allah be upon him).
Shaykh `Abd Al-Muhsin Al-`Abbad (may Allah preserve him) said: 
“When a person offers an Udhiyah , he does so on behalf of himself and the members of his household, and he may do so on behalf of the living and the dead among the members of his family. If a man leaves instructions (in his will) that an Udhiyah be offered on his behalf, then an Udhiyah should be offered on his behalf.
As for offering an Udhiyah on behalf of a deceased person only, we do not know of any proven evidence to support that practice. But if a person offers an Udhiyah on behalf of himself and the members of his household or his relatives, both living and dead, there is nothing wrong with that, and there is evidence in the Sunnah to support that. So the dead may be included alongside the living, but as for offering an Udhiyah on their behalf only, without them having left instructions to that effect, I do not know of any evidence for that.
With regard to the Hadith narrated by Abu Dawud from `Ali (may Allah be pleased with him), according to which he used to offer an Udhiyah of two rams and say that the Prophet (blessings and peace of Allah be upon him) had left instructions for him to do that, this is not proven from the Prophet (blessings and peace of Allah be upon him), because its chain of narrators includes a narrator who is unknown and another who was criticised (by the Hadith scholars) although he is not unknown. Anyone who wants to do something to increase the Prophet (blessings and peace of Allah be upon him), then he should strive to do righteous deeds for himself, for Allah, may He be Exalted, will give His Prophet (blessings and peace of Allah be upon him) a reward like that which He will give him, for the Prophet (blessings and peace of Allah be upon him) is the one who showed people the way to do good, and “Whoever guides to goodness will have a reward like that of the one who does it.” (End quote from Sharh Sunan Abu Dawud)
Even if we assume that the Hadith is authentic, this applies specifically to instructions left to be carried out after one’s death, as was clearly stated in the report of Abu Dawud. But the Prophet (blessings and peace of Allah be upon him) did not leave any instruction to anyone except `Ali (may Allah be pleased with him), so we must adhere to the texts and not go beyond that.
For more information on the ruling on offering an Udhiyah on behalf of a deceased person , please see the answer to question no. 36596
And Allah knows best.