Are the morning supplications accepted if they are recited after sunrise by someone who forgot them?

The morning remembrances (Adhkar al-Sabah) are not restricted by sunrise. Linguistically, "morning" (al-subh) refers to dawn (Fajr) and the beginning of the day. The best time for remembrance during the day is after the Fajr prayer, based on the Almighty's saying: ﴿And glorify the praises of your Lord before the rising of the sun and before its setting﴾ and the Prophet's (peace be upon him) saying: "Whoever prays Fajr in congregation, then sits remembering Allah Almighty until the sun rises, then prays two rak'ahs, will have a reward like that of a complete, complete, complete Hajj and 'Umrah (definition)."

Therefore, a Muslim can recite the morning remembrances upon waking up, as long as it is still within the morning time. Furthermore, the prophetic hadith (definition): "Whoever sleeps through his portion [of recitation] or part of it, and then recites it between the Fajr prayer and the Dhuhr prayer, it will be written for him as if he recited it during the night," indicates the desirability of maintaining regular litanies (awrad) and making them up if missed, and that performing them between the Fajr prayer and the Dhuhr prayer is like performing them during the night.