Are the remembrances mentioned in the bowing and rising from it among those authentically reported from the Prophet (peace and blessings be upon him)?

The sister's mention of a specific verbal remembrance during her bowing and after rising from it is not known to be from the Sunnah, nor have the jurists mentioned it. The best guidance is the guidance of Muhammad, peace and blessings be upon him. In bowing, it suffices to say "Subhan Allah" (Glory be to Allah), and in standing, to say "Rabbana wa lakal hamd" (Our Lord, and to You be all praise). The remembrance "Rabbana wa lakal hamd kama yanbaghi li jalali wajhika, wa atheemi sultanik" (Our Lord, and to You be all praise as befits the majesty of Your countenance and the greatness of Your dominion) was reported in a weak narration outside of prayer. Among the best forms of remembrance are: "Subhan Allah" (Glory be to Allah), "Alhamdulillah" (All praise is due to Allah), "La ilaha illallah" (There is no god but Allah), and "Allahu Akbar" (Allah is the Greatest).