This Hadīth has two narrations, and it is clear from the context that they were two occasions. The first narration tells about a man who came to the Prophet (may Allah's peace and blessings be upon him) and told him that his mother passed away without fasting one month that was due on her, so should he fast it on her behalf? The second narration is about a woman who came to the Prophet (may Allah's peace and blessings be upon him) and told him that her mother passed away without fasting a month that she vowed to fast, so should she fast on her behalf? In both cases, the Prophet told them that they should fast on behalf of their parents. The Prophet made an analogy to make the judgment clear by asking if their parents were indebted to a human being, would they pay their debts? They answered in the affirmative. The Prophet (may Allah's peace and blessings be upon him) told them that this fasting is a debt their parents owe to Allah. Since the debt to humans can be settled, the debt owed to Allah deserves more to be settled.
عمدة الأحكام، تأليف: عبد الغني بن عبد الواحد المقدسي، تحقيق: محمود الأرناؤوط، دار الثقافة العربية ومؤسسة قرطبة، الطبعة الثانية، 1408هـ. تيسير العلام، تأليف: عبد الله بن عبد الرحمن البسام، تحقيق محمد صبحي بن حسن حلاق، مكتبة الصحابة ومكتبة التابعين، الطبعة العاشرة، 1426 هـ. تنبيه الأفهام شرح عمدة الإحكام، تأليف: محمد بن صالح العثيمين، مكتبة الصحابة ومكتبة التابعين، الطبعة الأولى: 1426هـ. صحيح البخاري ، تأليف: محمد بن إسماعيل البخاري ، تحقيق: محمد زهير الناصر، الناشر: دار طوق النجاة الطبعة: الأولى، 1422هـ صحيح مسلم ، تأليف: مسلم بن الحجاج النيسابوري، تحقيق: محمد فؤاد عبد الباقي - الناشر: دار إحياء التراث العربي – بيروت.