Catalyzes two steps in the biosynthesis of the molybdenum cofactor. In the first step, molybdopterin is adenylated. Subsequently, molybdate is inserted into adenylated molybdopterin and AMP is released. adenylyl-molybdopterin + H(+) + molybdate = AMP + H2O + Mo-molybdopterin ATP + H(+) + molybdopterin = adenylyl-molybdopterin + diphosphate Inhibited by copper and tungsten. Cofactor biosynthesis; molybdopterin biosynthesis. The G domain: homotrimer or homohexamer. The E domain: homodimer. In the N-terminal section; belongs to the MoaB/Mog family. In the C-terminal section; belongs to the MoeA family.