Is it permissible to complete the fast of Monday with the intention of expiation for an oath after hesitation in the intention before Fajr?

Fasting on this day is not valid as an expiation for an oath, because expiatory fasting is an obligatory fast, which requires the intention to be made before Fajr, according to the Prophet, peace and blessings be upon him: "Whoever does not make the intention to fast before Fajr, then there is no fast for him." However, fasting on this day is valid as a supererogatory act, as the intention for a supererogatory fast can be made after Fajr, as long as one has not done anything to break their fast.