The fuqaha' are unanimously agreed that forgetting is an excuse which means that there is no sin or accountability in all matters, because of a great deal of evidence in the Qur'aan and Sunnah, but they differed as to whether the fidyah is still required in cases of forgetfulness.
With regard to the issue of forgetting to make up missed Ramadaan fasts before the next Ramadaan comes, the scholars are also unanimously agreed that they must still be made up after the second Ramadaan, and they are not waived as a result of forgetting.
But they differed as to whether the fidyah (which is feeding a poor person) is required when making up the missed fast (after the second Ramadaan has come and gone). There are two points of view:
1 - That the fidyah is not required, because forgetting is an excuse that means there is no sin and the fidyah is waived.
This was the view of most of the Shaafa'is and some of the Maalikis.
See: Tuhfat al-Muhtaaj by Ibn Hajar al-Haytami (3/445); Nihaayat al-Muhtaaj (3/196); Minah al-Jaleel (2/154); Sharh Mukhtasar Khaleel (2/263).
2 - That the fidyah is required, and forgetting is an excuse that means there is no sin only.
This was the view of al-Khateeb al-Sharbeeni among the Shaafa'is, who said in Mughni al-Muhtaaj (2/176):
It seems that it means there is no sin only, and that the fidyah is not waived.
This was also stated by some of the Maalikis.
See: Mawaahib al-Jaleel Sharh Mukhtasar Khaleel (2/450).
The more correct view is the former, in sha Allaah, for three reasons:
1 - The general meaning of the verses and ahaadeeth which say that people are not held accountable for forgetting, such as the verse in which Allaah says (interpretation of the meaning):
Our Lord! Punish us not if we forget or fall into error
2 - The basic principle that one is not subject to any expiation or fidyah except with evidence, and there is no reliable evidence in this case.
3 - There is a difference of opinion as to whether this fidyah is required in the first place, even in the case of one who delays making up the fasts deliberately. The Hanafis and Zaahiris are of the view that it is not obligatory and Shaykh Ibn Uthaymeen was of the view that it is only mustahabb, because there is no report to suggest that it is prescribed except from the actions of some of the Sahaabah, which is not strong enough to suggest that people be obliged to follow it, let alone oblige them to do it in a case where Allaah has granted an excuse.
See the answer to question no. 26865.
To sum up, he only has to make up the missed fasts, and he does not have to feed the poor, so he should make them up after Ramadaan.
And Allaah knows best.
Reproduced from Islam QA