Converts molybdopterin precursor Z into molybdopterin. This requires the incorporation of two sulfur atoms into precursor Z to generate a dithiolene group. The sulfur is provided by MoaD (By similarity). 2 [molybdopterin-synthase sulfur-carrier protein]-C-terminal Gly-NH-CH2-C(O)SH + cyclic pyranopterin phosphate + H2O = 2 [molybdopterin-synthase sulfur-carrier protein]-C-terminal Gly-Gly + 4 H(+) + molybdopterin Cofactor biosynthesis; molybdopterin biosynthesis. Heterotetramer of 2 MoaD subunits and 2 MoaE subunits. Also stable as homodimer. The enzyme changes between these two forms during catalysis (By similarity). Belongs to the MoaE family.