Is it considered that whoever prays Fajr in the mosque, then remembers Allah and memorizes the Qur'an until a quarter of an hour after sunrise, and then prays Duha, will have the reward of a complete Hajj and Umrah?

The apparent meaning of the hadith (definition) is that the reward for praying Fajr in congregation, then remembering Allah until sunrise, and then praying two rak'ahs, is contingent upon remaining in the same prayer place, whether at home or in the mosque. Whoever moves from their prayer place is not included in this promise. However, whoever intended to perform the act but was prevented from it will attain the reward due to their intention.