‘Ā'ishah (may Allah be pleased with her) reported that the Prophet (may Allah's peace and blessings be upon him) said: "Whoever dies while still having some fasts to make up for, his heir should fast on his behalf."
‘Ā'ishah (may Allah be pleased with her) informs that the Prophet (may Allah's peace and blessings be upon him) ordered the heir of the one who dies while still having some obligatory fasts to observe, such as a vow, expiation, or making up for missed Ramadan fasts; to fast on behalf of his deceased relative because it is a debt, and the relative is the worthiest of fulfilling his debt on his behalf. It is an act of kindness and dutifulness to him and from the maintenance of kinship ties. This command denotes desirability, not obligation.