All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The time of the morning Athkaar starts at the rise of dawn and ends shortly before noon, and the time of the evening Athkaar starts after noon and ends at midnight (when one half of the night has passed).
Shaykh Ibn 'Uthaymeen was asked, “When does the time of reciting the morning and evening Athkaar start and does it have an end time?"
He replied:
“It is known that the evening starts at noon and lasts until the middle of the night and that the morning starts at the rise of dawn and lasts until noon. However, the closer to dawn the morning Athkaar are recited, the more they are recited at their proper time, and the closer to the evening the evening Athkaar are recited, the more they are recited at their proper time. However, there are some Athkaar that should be recited after sunset (not before it) according to texts. For instance, the Prophet said, ‘Whoever recites Aayat Al-Kursi [Quran 2:255] at night...’ and, ‘Whoever recites the last two verses of Soorah Al-Baqarah at night, they would be sufficient for him.’ The important point is that all the Athkaar whose recitation is restricted to the night should be recited at night; what is not restricted to the night may be recited at any time in the evening, which is broad.” [Liqaa’ Al-Baab Al-Maftooh]
Hence, if you recite the morning Athkaar after the sunrise and the evening Athkaar after the sunset, you would be reciting them at their prescribed time and earn the consequent rewards and benefits, Allah willing.
Allah knows best.