Catalyzes the adenylation by ATP of the carboxyl group of the C-terminal glycine of sulfur carrier protein MoaD. [molybdopterin-synthase sulfur-carrier protein]-C-terminal Gly-Gly + ATP + H(+) = [molybdopterin-synthase sulfur-carrier protein]-C-terminal Gly-Gly-AMP + diphosphate Binds 1 zinc ion per subunit. Cofactor biosynthesis; molybdopterin biosynthesis. Homodimer. Forms a stable heterotetrameric complex of 2 MoeB and 2 MoaD during adenylation of MoaD (By similarity). Belongs to the HesA/MoeB/ThiF family.