Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) said that a woman came to the Prophet (peace and blessings be upon him) and said: "My mother has died and she owed the fasts of a vow." He (peace and blessings be upon him) said: "Would you pay off her debt if she had owed a debt?" She said: "Yes." He (peace and blessings be upon him) said: "Then fast on her behalf."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيام / 8227