Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) says that the Prophet (peace and blessings be upon him) seated Sayyiduna al-Fadl bin Abbas (may Allah be pleased with him) behind him on his mount, and al-Fadl was a handsome man. The Prophet (peace and blessings be upon him) stopped to give the people rulings, and a beautiful woman from the tribe of Khath'am turned towards him; she was asking the Prophet (peace and blessings be upon him) for a ruling. Al-Fadl looked at her, and her beauty pleased him. The Prophet (peace and blessings be upon him) looked at al-Fadl and saw that he was looking at the woman, so the Prophet (peace and blessings be upon him) took hold of al-Fadl's chin and turned his face to the other side. This Khath'ami woman said: "O Messenger of Allah! The obligation of Hajj has reached my father when he is a very old man, and he cannot sit on a mount; if I perform Hajj on his behalf, will it suffice?" The Prophet (peace and blessings be upon him) said: "Yes." [Sahih. Bukhari: 4138]
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9851
Sulayman bin Yasar narrates from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) that a woman from the tribe of Khath'am asked the Prophet (peace and blessings be upon him) on the morning of Muzdalifah, while Sayyiduna al-Fadl (may Allah be pleased with him) was riding behind him (peace and blessings be upon him). She said: The obligation of Hajj has reached my old father, and he cannot even stay seated on a mount; what is your (peace and blessings be upon him) view, may I perform Hajj on his behalf? He (peace and blessings be upon him) said: "Yes."
(b) Amr bin Dinar, narrating from Imam al-Zuhri before seeing Ibn Shihab, adds something to it: the woman said: Will it benefit him? He (peace and blessings be upon him) said: "Yes, it is just as if someone owed a debt and you paid it off."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9852
Sa'id bin Jubayr (may Allah have mercy on him) narrates from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) that a man came to the Prophet (peace and blessings be upon him) and said: My sister vowed to perform Hajj, but she has died. He (peace and blessings be upon him) said: "If she had owed a debt, would you have paid it?" He said: Yes. He said: "Then fulfil what is owed to Allah, for He is more deserving of fulfilment."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9853
Sa'id bin Jubayr (may Allah have mercy on him) says that a man passed by Ibn Abbas (may Allah be pleased with them both) reciting the talbiyah for Hajj on behalf of Shubrumah. He asked: Who is Shubrumah? He said: He made a bequest that Hajj be performed on his behalf. He asked: Have you performed Hajj for yourself? He said: No. Ibn Abbas (may Allah be pleased with them both) said: First perform Hajj for yourself, then perform it on behalf of Shubrumah.
(b) Ata (may Allah have mercy on him) says that a man may perform Hajj on behalf of his father even if he did not make a bequest.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9854
Sayyiduna Jabir bin Abdullah (may Allah be pleased with them both) says that the Messenger of Allah (peace and blessings be upon him) said: "Through a single Hajj, Allah will admit a group of three people into Paradise: (1) the deceased, (2) the one who performs Hajj on his behalf, and (3) the one who carries it out (the executor)."
Abu Ma'shar here is Najih al-Sindi, a Madinan, and he is da'if (weak).
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9855
Anas bin Malik (may Allah be pleased with him) says that the Messenger of Allah (peace and blessings be upon him) said about a man who had made a bequest for Hajj: "Four Hajjs are recorded for it: (1) a Hajj for the one who wrote it, (2) a Hajj for the one who carried it out, (3) a Hajj for the one who undertook it, and (4) a Hajj for the one who ordered it."
This Ziyad bin Sufyan is majhul (unknown), and the chain is da'if (weak). Reports have also been narrated about performing Hajj on behalf of parents with weak chains, so I have left them out; and some of what we have narrated is sufficient. And success is from Allah.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9856