Does one who catches the Imam in the second rak'ah of Fajr, then sits until sunrise, receive the reward mentioned in the famous hadith?

Whoever catches the second raka'ah of the Fajr prayer with the Imam has caught the congregational prayer, based on the saying of the Prophet, peace and blessings be upon him: "Whoever catches one raka'ah of the prayer has caught the prayer." And if he sits in his place of prayer remembering Allah until the sun rises, then prays two rak'ahs, it is hoped that he will attain the reward of a Hajj and an 'Umrah, based on the saying of the Prophet, peace and blessings be upon him: "Whoever prays Fajr in congregation, then sits remembering Allah until the sun rises, then prays two rak'ahs, it will be for him like the reward of a Hajj and an 'Umrah." He said: The Messenger of Allah, peace and blessings be upon him, said: "Complete, complete, complete."