If the Fajr prayer is missed and one wakes up late, should it be made up at the time of the Dhuhr prayer on the same day, or on the following day with the Fajr prayer? And what is the validity of the statement that a missed prayer is made up at its corresponding time on the following day (such as making up the Asr prayer with the next Asr prayer)?

Prayer is a great pillar of Islam, and it is the first thing a Muslim will be held accountable for. Whoever sleeps through an obligatory prayer until its time has passed, must make it up immediately upon waking up; for the Prophet, peace and blessings be upon him, said: "If one of you oversleeps or is heedless of a prayer, he should pray it when he remembers it, for Allah says: 'Establish prayer for My remembrance.'" He should not delay making it up until the next day.