Are the prayers of someone who became ritually impure then prayed, forgetting, and the time for prayers expired, accepted?

If you are certain or highly assume that the seminal emission (ihtilam) occurred during the first sleep, then you must perform ghusl (definition) (ritual bath) and re-pray the Maghrib, Isha, and Fajr prayers. However, if you are unsure about the time of the seminal emission, consider that it happened during the second sleep. In this case, you are only required to perform ghusl and re-pray the Fajr prayer, because an event is attributed to its nearest time. An invalid prayer does not cease to be due by the passing of its time; rather, it remains an obligation until it is performed. A prayer that is free from invalidating factors is sufficient and discharges one's responsibility, but its acceptance by Allah is a matter of the unseen. One must take the necessary measures to wake up for prayer if there is a fear of missing it due to sleep.