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: O Messenger of Allah! My sister vowed to fast for a month; she was travelling by sea and died, and she had not observed those fasts. So he (peace and blessings be upon him) said to her: "Fast on behalf of your sister." These words are proof of fasting on her behalf.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيام / 8226