Time for Morning Adhkar
Question

If I forgot to say Adhkar As-Sabah (words of remembrance for the morning) before sunrise, is it acceptable if I say them whenever I wake up?
Praise be to Allah.Time for Morning Adhkar
Adhkar As-Sabah (supplications recited in the morning) are not connected only to the time when the sun rises; in Arabic the word Subh (morning) applies to dawn and the first part of the day, as is stated in the dictionary: Al-Qamus Al-Muhit (291). Allah Says (interpretation of the meaning):
{… and celebrate the praises of your Lord in the evening and in the morning.} [Ghafir 40:55]
Best Time for Morning Adhkar
Ibn Kathir (may Allah have mercy on him) said in his Tafsir  (exegesis) (4/86) that this means in the early part of the day and in the early part of the night. But the best time of the day for making Dhikr (reciting words of remembrance) is after the dawn prayer, because Allah Says (interpretation of the meaning):
{… and glorify the praises of your Lord before the rising of the sun, and before its setting…} [Taha 20:130]
Moreover, the Prophet (peace and blessings of Allah be upon him) said: “Whoever prays Fajr in congregation, then sits and remembers Allah (makes Dhikr) until the sun rises, then prays two Rak`ahs (units of prayer), will have a reward like that for Hajj and ‘Umrah (major and minor Pilgrimage), complete, complete, complete.” (Sahih Al-Jami`, 6222)
Recommended Adhkar for the Morning
Based on the above, this is how we understand the reports narrated on this topic, such as the Hadiths:
“Whoever says, in the morning and the evening , ‘Subhan Allahi wa bi hamdih (Glory and praise be to Allah)’ one hundred times, will not come with anything better than it on the Day of Resurrection, except for one who does likewise or does more.” (Narrated by Muslim, 2692)
“Allahumma bika asbahna wa bika amsayna wa bika nahya wa bika namut wa ilayka An-nushur (O Allah, by Your blessings we reach the morning, by Your blessings we reach the evening, by Your blessings we live, by Your blessings we die, and unto You is the Resurrection).” (Narrated by Abu Dawud in As-Sunan, 5068 and An-Nasa’i in As-Sunan Al-Kubra, 9836. Al-Albani said it is an authentic narration).
Therefore, you can say Adhkar As-Sabah when you wake up from sleeping, because it is still the time of morning. And Allah is the Source of strength.
Making Up Missed Dhikr
Muslim narratedin his Sahih (no. 747) that the Prophet (peace and blessings of Allah be upon him) said: “Whoever sleeps without doing his regular Dhikr or part of it, then recites it during the time between the Fajr prayer and Dhuhr prayer, it will be recorded as if he had recited it at night.”
In Sharh Muslim (6/27), An-Nawawi (may Allah have mercy on him) said:
“This indicates that it is preferred to recite Awrad (dhikr, supplications) regularly, and that if one misses it, one can make it up later.”
In `Awn Al-Ma`bud (4/198) it says: “This Hadith indicates that it is permissible to recite Wird (singular of Awrad) regularly at night, and that it is permissible to make it up if one misses it because of sleeping or any other reason. It also indicates that the one who does this between the Fajr prayer and Dhuhr prayer is like the one who does it at night, so it is recommended to make up Tahajjud (optional night prayers) if one misses it at night.”
For more details, please see the following answers: 126587 , 194998 , 22765 .
And Allah knows best.