Catalyses the synthesis of molybdopterin from cyclic pyranopterin monophosphate. Two sulfur atoms are transferred to cyclic pyranopterin monophosphate in order to form the characteristic ene-dithiol group found in the molybdenum cofactor. Molybdopterin synthase consists of two large subunits forming a central dimer and two small subunits (molybdopterin-synthase sulfur-carrier proteins) that are thiocarboxylated at the C-terminus by EC
2.8.1.11, molybdopterin synthase sulfurtransferase. The reaction occurs in prokaryotes and eukaryotes.