Reference: http://mufti.af.org.sa/ar/content/من-يتأخر-في-القضاء-آثم-ويلزمه-القضاء-والتوبة
Question: I was careless in making-up some of the days which I was required to fast from the previous [month of] Ramadhaan until the arrival of the following month [of Ramadhaan]; so what am I [now] required to do?
Response: In principle, Allaah (Jalla wa ‘Alaa) has told us:
…so Allaah has permitted the traveller not to fast, and has legislated for him to make-up [the missed days] on other days [after Ramadhaan has passed].
[Importantly], He did not stipulate [for them to be made-up during] a particular month, rather [any time] from Shawwaal through to the [end of the] next [month of] Sha’baan – all of it is open to choice.
And if the number of days remaining in Sha’baan are equal to the number of days of Ramadhaan required to be made-up, then he is required to hasten in making-up [these days]. And if he does not do so, then he has sinned, and he is then required to make-up those [remaining] days after [the passing of] the coming Ramadhaan as well as feeding a poor and needy person for each day remaining to be made-up; in addition he must turn to Allaah in repentance for the delay [in making-up the missed days] without [an Islaamically acceptable] reason.