Is the fast of one who intended to fast at night, then forgot and broke his fast after Fajr, then remembered and completed his fast, valid? And does the hadith: "Whoever forgets while he is fasting and eats or drinks, then let him complete his fast, for it was Allah who fed him and gave him drink," apply to him?

Whoever intends to fast on Wednesday night is considered fasting from Fajr, and their forgetfulness of the intention after Fajr does not harm their fast, as long as they do not intend to break it. If they eat forgetfully after Fajr, they may complete their fast, based on the Prophet's (peace and blessings be upon him) saying: "Whoever forgets while he is fasting, and eats or drinks, let him complete his fast, for indeed Allah has fed him and given him drink." This ruling applies to fasting in Ramadan (definition), qada' (making up missed fasts), vows, and supererogatory fasts.