Catalyzes the insertion of molybdate into adenylated molybdopterin with the concomitant release of AMP. adenylyl-molybdopterin + H(+) + molybdate = AMP + H2O + Mo-molybdopterin Binds 1 Mg(2+) ion per subunit. Cofactor biosynthesis; molybdopterin biosynthesis. Homodimer. Interacts with MobA, MogA and MobB in vivo. Belongs to the MoeA family.