Component of the dihydroxyacetone kinase complex, which is responsible for the phosphoenolpyruvate (PEP)-dependent phosphorylation of dihydroxyacetone. DhaM serves as the phosphoryl donor. Is phosphorylated by phosphoenolpyruvate in an EI- and HPr-dependent reaction, and a phosphorelay system on histidine residues finally leads to phosphoryl transfer to DhaL and dihydroxyacetone