Is it permissible to count the days that were fasted to make up for the first Ramadan – which later became clear required no making up – as making up for the days of the other Ramadan?

If a person has missed fasts from two Ramadans or more, they are not required to specify the intention for the particular day being made up, as long as the fasting is of the same type. So, if they fast with the intention of making up what is due without specifying, and then it becomes clear that the first Ramadan did not require a make-up, then the fasting counts for the second Ramadan. However, if they specified the intention for fasting the first Ramadan, and then it becomes clear that it did not require a make-up, then it does not count for making up the second Ramadan; because the intention cannot be changed after the completion of the act of worship. This applies generally to all acts of worship.