Died whilst still having days to make up from Ramadhaan
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Question: What is the ruling of one who has died whilst still having had days to make up from Ramadhaan?

Response: If he has died whilst still having days to make up from Ramadhaan, then the one who is in charge of his affairs from amongst his close relatives or inheritors should fast on his behalf. That which is mentioned in the hadeeth by 'Aa.ishah is that the Prophet (sal-Allaahu `alayhe wa sallam) said: ((One who has died whilst having days to make up from Ramadhaan, then the one who is in charge of his affairs must fast on his behalf)). If the one who is in charge of his affairs does not fast on his behalf then he must feed a poor person for every day (to be made up).

Shaykh Ibn 'Uthaymeen
Fataawa Ramadhaan - Volume 2, Page 626, Fatwa No. 626;
Fiqh al-'Ibaadaat libni 'Uthaymeen - Pages 202-203