Does the prayer of one who says, "God heard him who praised Him," instead of "Our Lord, to You be praise," after the Imam says, "God heard him who praised Him," then says, "Our Lord, to You be praise," after standing upright, invalidate his prayer due to his ignorance of the correct place for the ذكر (remembrance)?

The majority of scholars hold that the congregant should only say "Rabbana wa lakal-hamd" (Our Lord, to You be all praise) upon rising from rukūʿ. The Shāfiʿīs and some Ḥanbalīs are of the view that the congregant says "Samiʿa Allāhu liman ḥamidah" (Allah hears the one who praises Him) upon rising from rukūʿ, and then says "Rabbana lakal-hamd" (Our Lord, to You be all praise) when standing upright. In these two recitations, the imām, the congregant, and the one praying alone are equal. As for saying "Samiʿtu Allāha liman ḥamidah" (I heard Allah hears the one who praises Him), it is a linguistic error (laḥn) but does not invalidate the prayer. Therefore, your prayer is valid.