Catalyzes the first step of diphthamide biosynthesis, i.e. the transfer of the 3-amino-3-carboxypropyl group from S-adenosyl-L-methionine (SAM) to the C2 position of the imidazole ring of the target histidine residue in translation elongation factor 2 (EF-2). 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. Homodimer. Unlike the enzymes in the radical SAM superfamily, Dph2 does not form the canonical 5'-deoxyadenosyl radical. Instead, it breaks the C(gamma)-S bond of SAM and generates a 3-amino-3-carboxypropyl radical intermediate. Belongs to the DPH1/DPH2 family.