As for the one who dies while still owing fasts…
The author says: “They are likewise unanimously agreed that if a person is unable to fast, no one may fast on his behalf during his lifetime.”
I reply: It appears that there is in fact no consensus on this point, for Ibn Taymiyyah dissented. In al-Ikhtiyārāt (p. 64) he writes:
“If someone volunteers to fast on behalf of a person who is unable to fast because of old age and the like, or on behalf of a deceased person—when both parties are of limited means—the permissibility of that should be considered, for fasting is closer in kind to the original obligation than is giving money in charity. Al-Qāḍī has transmitted a similar view regarding the fast of a vow while the one who made the vow is still alive.”
I mention this only by way of information, not endorsement, for I do not regard it as correct; it conflicts with the verse, “and that man will have nothing but what he strives for” (53:39). Ibn Taymiyyah interprets the verse so as not to oppose his position, but this is not the place to elaborate; whoever wishes may consult his discussion for further detail.
The author then cites the preferred Shāfiʿī opinion: that it is recommended for the guardian of the deceased to fast on his behalf. They adduce the report recorded by Aḥmad and the two Ṣaḥīḥs from ʿĀʾishah in which the Prophet ﷺ said, “Whoever dies while liable for fasts, his guardian should fast on his behalf.” Al-Bazzār adds the wording, “if he so wishes,” and comments that its chain is sound.
I say: On the contrary—this additional wording is weak and objectionable. It rests on Ibn Luhayʿah, who is weak, and he alone transmits it, as Ibn Ḥajar states in Fatḥ al-Bārī and in at-Talkhīṣ: “It is weak because it comes through the route of Ibn Luhayʿah.”
The present author seems to have followed Ṣiddīq Khān in al-Rawḍah in grading it sound, and Ṣiddīq Khān, in turn, followed al-Haythamī.