後の世
(後世の意味なら)after ages―posterity―(来世の意味なら)―the future life―the next world
後の世に伝わる
後の世に伝える
to hand something down to the next generation
He is designed for something great―He has a great future before him―He has in him the making of a great man―(女なら)―She has in her the making of a beautiful woman.