Do the days made up with the intention of making up the first Ramadan suffice for the days of the third Ramadan?

Firstly: Whoever has missed days from past Ramadans must make them up in sequential order, according to Imam Ahmad, starting with the oldest. However, the majority of scholars are of the opinion that sequential order is not obligatory.

Secondly: If someone fasts with the intention of making up for the first Ramadan, and then it becomes clear that there is no make-up due for it, then what he has fasted cannot be redirected to make up for the third Ramadan. This is based on the Prophet's (peace be upon him) saying: "And indeed, for every person is what he intended." The intention was directed towards the first Ramadan, and there is no consideration for changing the intention after the act of worship has been performed. If the intention had been absolute (unspecified), then it would have been valid to redirect the make-up to the third Ramadan.