Catalyzes the cyclization of 2-amino-4,5-dihydroxy-6-one-heptanoic acid-7-phosphate to yield 3-amino-4-hydroxybenzoic acid (3,4-AHBA). 2-amino-4,5-dihydroxy-6-oxo-7-(phosphooxy)heptanoate = 3-amino-4-hydroxybenzoate + H(+) + 2 H2O + phosphate Monomer. Belongs to the archaeal-type DHQ synthase family. GriH subfamily.