Cyclotransferase that catalyzes the last step in the biosynthesis of the aminoglycoside antibiotic butirosin B. Cleaves the amide bond via transamidation using the alpha-amine of the terminal gamma-L-glutamate of the side chain, releasing it as the cyclic 5-oxoproline. gamma-L-glutamyl-butirosin B = 5-oxo-L-proline + butirosin B Antibiotic biosynthesis; butirosin biosynthesis. Belongs to the gamma-glutamylcyclotransferase family.