.Regarding this issue, a Muslim is encouraged to hurry to make up for the missed fast days of Ramadan for no one knows when he or she will die. It is allowed to make up for the missed fast days of Ramadan in any month that comes after Ramadan before the coming of other Ramadan. However if one became late in making up for the missed fasts until the next Ramadan came, some scholars are of the opinion that he/she has to make up for the missed fasts along with a ransom. But other Muslim scholars are of the opinion that ransom is not obligatory, instead, he/she has to make up for the missed fasts only.
Elaborating on this issue, the eminent Muslim scholar Sheikh Yusuf Al-Qaradawi states the following:
“A Muslim male or female should make up for the missed obligatory days of Ramadan whenever he or she can. The missed fast days are to be offered at any time of the year before the coming of the next Ramadan. This implies that there are eleven months for a Muslim to make up for the missed fast days, whether the obligatory fast of Ramadan was broken due to illness, travel, menses, or any other valid reasons.
Therefore, there is flexibility in Islamic Sharia regarding when one is permitted to make up for the missed fast days. One can make up for the missed fast days in Shawwal, that is, right after Ramadan, and also in the months that follow.
Undoubtedly, it is advised to speed up in making up for the missed fast days. Allah says about hastening in doing good: (… so vie with one another in good works) (Al-Ma’idah 5: 48).
Further more, it is better for one to make up for missed days because nobody knows when his end will come. In case one delays making up for the missed fast days, whether because of hot climate, weakness, or a physical ailment, or because one is preoccupied with certain duties preventing one from observing fast, then one has time until the next Ramadan.
When Sha`ban comes, one should make up for the missed days, for it is one’s last chance before entering the next Ramadan.
Having clarified the above, I should add here that making up for missed fast days of Ramadan can be delayed and performed later whenever a person is able; this is in cases when the person remains sick until next Ramadan. Hence, making up for the fast days will be like a debt that one should pay whenever one becomes able. Doing so is permissible, where Allah says by the end of a Qur’anic verse about fasting: (Allah desires for you ease; He desires not hardship for you) (Al-Baqarah 2: 185).”
As for making up for the missed fasts after the passage of other Ramadan,Sheikh Yusuf Al-Qaradawi adds:
“Some scholars say that if you miss some days of Ramadan and another Ramadan comes before making up for those missed days from the previous Ramadan, then you have to make up for them along with a ransom. The ransom is to feed a poor person one mudd from the predominant foodstuff of the country for each day. The mudd is approximately a little more than half a kilogram. This is the madh-hab (school) of the Shafi`is and the Hanbalis who act upon certain practices ascribed to some of the Companions.
The other Imams and scholars do not make this an obligation. All in all, if this happens with a man, then he is to definitely make up for the fast days. As for feeding someone or giving a ransom, if he does this then he has done something good and if he abandons it then by the will of Allah there will be no blame on him. That is because there is nothing authentic from the Prophet (peace and blessings be upon him) concerning this.”