S-adenosyl-L-methionine-dependent methyltransferase that catalyzes the trimethylation of the amino group of the modified target histidine residue in translation elongation factor 2 (EF-2), to form an intermediate called diphthine. The three successive methylation reactions represent the second step of diphthamide biosynthesis. 2-[(3S)-amino-3-carboxypropyl]-L-histidyl-[translation elongation factor 2] + 3 S-adenosyl-L-methionine = diphthine-[translation elongation factor 2] + 3 H(+) + 3 S-adenosyl-L-homocysteine Protein modification; peptidyl-diphthamide biosynthesis. Homodimer. The diphthine intermediate is not stable in vitro and readily eliminates the trimethylamino group. It is not known whether the elimination reaction also occurs physiologically. Belongs to the diphthine synthase family.