Is the intention for a make-up fast (qada') valid if the intention for fasting was specified two days before the fast, then the intention was recalled on the morning of the fast day?

Regarding make-up fasting (qaḍāʾ), it is essential, according to the majority of scholars, to form the intention from the night before. If you do not form the intention from the night before, your fast is considered a supererogatory (nafl) fast if you intended it during the day before breaking the fast, and you would still be required to make up the missed day. However, if you drank before intending to fast, your fast is not valid, neither as an obligatory (farḍ) nor a supererogatory fast.