A wheat variety designated 6PUMH97B, the plants and seeds of wheat variety 6PUMH97B, methods for producing a wheat plant produced by crossing the variety 6PUMH97B with another wheat plant, and hybrid wheat seeds and plants produced by crossing the variety 6PUMH97B with another wheat line or plant, and the creation of variants by backcrossing, mutagenesis or transformation of variety 6PUMH97B are disclosed. Methods for producing other wheat varieties or breeding lines derived from wheat variety 6PUMH97B and to wheat varieties or breeding lines produced by those methods are also provided.