✅ Answer: Please pay attention to the following narrations:

1 عَنْ مُحَمَّدٍ يَعْنِي الصَّفَّارَ قَالَ: كَتَبْتُ إِلَى الْأَخِيرِ رَجُلٌ مَاتَ وَ عَلَيْهِ قَضَاءٌ مِنْ شَهْرِ رَمَضَانَ- عَشَرَةُ أَيَّامٍ وَ لَهُ وَلِيَّانِ هَلْ يَجُوزُ لَهُمَا أَنْ يَقْضِيَا عَنْهُ جَمِيعاً خَمْسَةَ أَيَّامٍ أَحَدُ الْوَلِيَّيْنِ وَ خَمْسَةَ أَيَّامٍ الْآخَرُ فَوَقَّعَ يَقْضِي عَنْهُ أَكْبَرُ وَلِيَّيْهِ عَشَرَةَ أَيَّامٍ وِلَاءً إِنْ شَاءَ اللَّهُ.

📚 Al-Kafi Vol. 4, p. 124

Saffar said: I wrote a letter to the latter (i.e., Imam Hasan Askari, peace be upon him): A man dies and he owes ten days of missed fasts from the month of Ramadan, and he has two guardians. Is it permissible for both of them to make them up, in this way that one of them makes up five days and the other also five days? The Imam replied in writing: The elder of the two guardians will make up the ten days consecutively on his behalf. Insha'Allah.

📚 Al-Kafi Vol. 4, p. 123

2 عَنِ ابْنِ أَبِي عُمَيْرٍ عَنْ حَفْصِ بْنِ الْبَخْتَرِيِّ عَنْ أَبِي عَبْدِ اللَّهِ فِي الرَّجُلِ يَمُوتُ وَ عَلَيْهِ صَلَاةٌ أَوْ صِيَامٌ قَالَ يَقْضِي عَنْهُ أَوْلَى النَّاسِ بِمِيرَاثِهِ قُلْتُ فَإِنْ كَانَ أَوْلَى النَّاسِ بِهِ امْرَأَةً فَقَالَ لَا إِلَّا الرِّجَالُ.

Imam Sadiq (peace be upon him) said about a person who dies and has missed prayers or fasts to make up: The person most deserving of his inheritance makes them up on his behalf. I said: What if the person most deserving of his inheritance is a woman? He said: No, only from the men.

📚 Al-Bihar Vol. 88, p. 313

Imam Sadiq (peace be upon him) said: The prayer whose time has entered before the deceased person dies, the person most deserving of his inheritance makes it up on his behalf.

3 عَنْ عَبْدِ اللَّهِ بْنِ سِنَانٍ عَنِ الصَّادِقِ قَالَ: الصَّلَاةُ الَّتِي دَخَلَ وَقْتُهَا قَبْلَ أَنْ يَمُوتَ الْمَيِّتُ يَقْضِي عَنْهُ أَوْلَى النَّاسِ بِهِ.

✅ According to the above narrations and others, the missed prayers and fasts of the deceased are obligatory upon the person most deserving of his inheritance or the elder of his male guardians.

In the case of this question, where the person has two twin sons, the above ruling applies. But to determine which of these two sons is older, we need the following narration:

📚 Al-Kafi Vol. 6, p. 53

A person had two twin sons born to him in one womb. Imam Sadiq (peace be upon him) congratulated him and then said: Which one is older? He said: The one who was born first! The Imam said: The one who was born second is older! Do you not know that (this second one) was first conceived, and then the other one entered upon him, and the exit of the first is not possible until this one first exits, so the one who was born second is the elder of these two twin children!

4 عَنْ مُحَمَّدِ بْنِ يَحْيَى عَنْ أَحْمَدَ بْنِ مُحَمَّدِ بْنِ عِيسَى عَنْ عَلِيِّ بْنِ أَحْمَدَ بْنِ أَشْيَمَ عَنْ بَعْضِ أَصْحَابِهِ قَالَ: أَصَابَ رَجُلٌ غُلَامَيْنِ فِي بَطْنٍ فَهَنَّأَهُ أَبُو عَبْدِ اللَّهِ ثُمَّ قَالَ أَيُّهُمَا الْأَكْبَرُ فَقَالَ الَّذِي خَرَجَ أَوَّلًا فَقَالَ أَبُو عَبْدِ اللَّهِ الَّذِي خَرَجَ أَخِيراً هُوَ أَكْبَرُ أَ مَا تَعْلَمُ أَنَّهَا حَمَلَتْ بِذَاكَ أَوَّلًا وَ أَنَّ هَذَا دَخَلَ عَلَى ذَاكَ فَلَمْ يُمْكِنْهُ أَنْ يَخْرُجَ حَتَّى خَرَجَ هَذَا فَالَّذِي يَخْرُجُ أَخِيراً هُوَ أَكْبَرُهُمَا.

✅ According to the above narration, the obligation to perform the deceased's missed prayers and fasts falls upon the son who was born last.

✅ Of course, according to the following hadith, the other son can also perform the father's missed prayers and fasts, but the obligation and necessity of this task are on the elder male guardian:

Al-Faqih Vol. 2, p. 153

Shaykh Saduq said: It is narrated from Imam Sadiq (peace be upon him) that he said: When a person dies and has missed fasts from the month of Ramadan, anyone from his family who wishes can make them up on his behalf.

Missed Prayer

5 مُحَمَّدُ بْنُ عَلِيِّ بْنِ الْحُسَيْنِ قَالَ قَدْ رُوِيَ عَنِ الصَّادِقِ أَنَّهُ قَالَ: إِذَا مَاتَ الرَّجُلُ وَ عَلَيْهِ صَوْمُ شَهْرِ رَمَضَانَ- فَلْيَقْضِ عَنْهُ مَنْ شَاءَ مِنْ أَهْلِهِ.

اللَّهُمَّ فَصَلِّ عَلَی مُحَمَّدٍ وَ آلِ مُحَمَّدٍ وَ عَجِّلْ لِوَلِیِّکَ الْفَرَجَ وَ الْعَافِیَةَ وَ النَّصْرَ