Hawzah News Agency – If someone goes to sleep before the time of ṣubḥ prayers in Ramadan – or on any day which he assigned for keeping an obligatory (wājib) fast – without making the intention to fast, and he wakes up before midday (ẓuhr) and makes the intention to fast, his fast is valid. However, if he wakes up after ẓuhr, he must, as a precautionary measure, abstain [from the eight things that invalidate a fast] for the rest of the day with a general intention of attaining proximity to Allah (qaṣd al-qurbah al-muṭlaqah) [i.e. with the intention of attaining proximity to Allah without specifying any particulars about the fast], and he must also keep a qaḍāʾ fast for it [i.e. he must make up a fast for it after Ramadan].

Source: https://www.sistani.org/english/book/48/