بسم الله الرحمن الرحيم
All Praises are for Allah Lord of all that exists and peace and blessings of Allah be on His final Messenger and his household.
A Muslim must make up the fasting for all the days he (includes “she” in Fiqhi discussions unless otherwise specified) has missed during the Month of Ramadhan. Allah SWT says (as translated): and whoever is ill or on a journey – then an equal number of other days. (2:184)
Making up the missed days can be done consecutively or separately and this is the opinion of the Four Schools of Fiqh, namely: Hanafi, Maliki, Shafe’I and Hanbali
While the time to make up the fasts lasts until the end of the next Sha’baan, it should be done as early as possible so long he has the ability to do so.
If he delays making up the fast till after the next Ramadhan without a valid reason, then he should feed a poor person for every day missed and also make it up the fasting which he has not done the previous year.
On the other hand, if he delays it for a valid reason, then he just make up for the missed days by fasting only and does not have to feed a poor for every day missed.
Those who become conscious of the obligation of Fasting and has many days or perhaps months to make up for Ramadhans missed then if he can fast them that would be the best.
If it is too burdensome for him to fast all, then he can fast some and pay Fidya (feeding a poor person for everyday missed) for the remaining days or simply pay Fidya for all what was missed. If he cannot even do that, he makes Tawbah and strive not to let this happen to him again.