Catalyzes the first step of diphthamide biosynthesis, a post-translational modification of histidine which occurs in elongation factor 2. DPH1 and DPH2 transfer a 3-amino-3-carboxypropyl (ACP) group from S-adenosyl-L-methionine (SAM) to a histidine residue, the reaction is assisted by a reduction system comprising DPH3 and a NADH-dependent reductase, predominantly CBR1. L-histidyl-[translation elongation factor 2] + S-adenosyl-L-methionine = 2-[(3S)-amino-3-carboxypropyl]-L-histidyl-[translation elongation factor 2] + H(+) + S-methyl-5'-thioadenosine Binds 1 [4Fe-4S] cluster per subunit. The cluster is coordinated with 3 cysteines and an exchangeable S-adenosyl-L-methionine. Protein modification; peptidyl-diphthamide biosynthesis. Component of the 2-(3-amino-3-carboxypropyl)histidine synthase complex composed of DPH1, DPH2, DPH3 and a NADH-dependent reductase, predominantly CBR1. Belongs to the DPH1/DPH2 family. DPH1 subfamily.