What is better to do after Fajr prayer in the mosque until sunrise: reciting the Qur’an or morning remembrances (adhkar al-sabah)?

It is better to busy oneself with the morning remembrances (adhkar) because they are time-bound, and the Sunnah is to perform them within their designated time. Once finished with them, it is better to engage in reading the Quran, as it is the best of unrestricted remembrances.