Muwatta Imam Malik (Riwayat Yahya)

It is narrated from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them) that Sayyiduna Sa'd bin Ubadah (may Allah be pleased with him) asked the Messenger of Allah (peace and blessings of Allah be upon him) that my mother has passed away and she had a vow due upon her which she did not fulfill. The Prophet (peace and blessings of Allah be upon him) said: "Fulfill it on her behalf."

It is narrated from Abdullah bin Abi Bakr that he heard from his paternal aunt, who stated that her grandmother had made a vow to go to the Mosque of Quba on foot, but she died and did not fulfill that vow. So, Abdullah bin Abbas (may Allah be pleased with them both) instructed her daughter to fulfill that vow on her behalf.

Imam Malik, may Allah have mercy on him, said: No one should fulfill a vow to walk on behalf of someone else.

It is narrated from Abdullah bin Abi Habibah that I said to a person, and I was young at the time, that if someone only says «عَلَيَّ مَشْيٌ إِلَى بَيْتِ اللّٰهِ» meaning, "It is upon me to walk to the House of Allah," and does not say, "It is a vow upon me to walk to the House of Allah," then nothing becomes obligatory upon him. That person said to me, "I have this cucumber in my hand, I give it to you, so just say, 'It is upon me to walk to the House of Allah.'" I said, "Yes, I will say it," so I said it, and I was young. Then, after a short while, I came to my senses and people said to me that walking to the House of Allah has become obligatory upon you. I went to Sa'id bin al-Musayyib and asked him, and he also said that walking to the House of Allah has become obligatory upon you, so I walked to the House of Allah.
Imam Malik, may Allah have mercy on him, said: This is the ruling according to us.