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 Cofactor biosynthesis; molybdopterin biosynthesis. Belongs to the HesA/MoeB/ThiF family.