Muslim

Hadith Commentary:
The position of the Ahl al-Hadith is in accordance with the hadith of the chapter, that the guardian should fast on behalf of the deceased, and this is also the old opinion (qawl qadim) of Imam Shafi'i.
Imam Shafi'i, as narrated by al-Bayhaqi with a sound chain, said: "When an authentic hadith reaches you that contradicts my statement, then act upon the hadith and do not follow me in imitation." Imam Malik and Abu Hanifah rahimahullah, contrary to this authentic hadith, held the view that no one can fast on behalf of another.
(Wahidi)

Shah Waliullah Muhaddith Dehlawi:
Regarding fasting on behalf of the deceased, he states that there are two secrets in this matter. One is with respect to the deceased, because many souls, when they part from their bodies, remain aware that some act of worship which was obligatory upon them and for the abandonment of which they will be held accountable, has been missed. Therefore, those souls remain in a state of grief and distress, and as a result, the door of dread is opened upon them. At such a time, the greatest compassion for them is that the person among the people who is closest to the deceased should perform such an act and intend that "I am performing this act on his behalf." This proves beneficial for the relative of that person, or that person performs some other act similar to it. Likewise, if a person had intended to give charity (sadaqah) but died without giving it, then his heir should give charity on his behalf.
(Hujjat Allah al-Baligha)

Hadith Commentary:
(1)
In the hadith, "alayhi siyam" refers not to voluntary (nafl) fasts, but rather to those fasts which are obligatory upon a person, such as:
٭ The fasts of Ramadan.
٭ Fasts vowed (nazr).
٭ Fasts of expiation (kaffarah).
If a person passes away and has obligatory fasts pending, then his heir must make arrangements for those fasts.
In some narrations, there is an addition:
If the heir wishes, he may fast.
But this narration is weak.
(al-Talkhis al-Habir: 6/457)
Imam al-Bayhaqi writes in "Khilaafiyat":
There is no difference of opinion among the hadith scholars on this issue.
(Fath al-Bari: 4/246)
(2)
Some scholars hold the view that instead of the heir fasting on behalf of the deceased, he should feed one needy person for each missed fast.
Their evidence is the following narration:
The Messenger of Allah (sallallahu alayhi wa sallam) said:
"Whoever dies while he has fasts due upon him, then for each day, a needy person should be fed on his behalf."
(Sunan Ibn Majah, al-Siyam, Hadith: 1757)
But this narration, due to its weakness, is not a valid proof.
(Da'if Sunan Ibn Majah, al-Siyam, Hadith: 389)
In some narrations, it is stated that no one should fast on behalf of another.
(al-Muwatta' of Imam Malik, al-Siyam: 1/279, Hadith: 688)
What is meant by this is general voluntary (nafl) fasts.