Catalytic subunit of the molybdopterin synthase complex, a complex that catalyzes the conversion of precursor Z into molybdopterin. Acts by mediating the incorporation of 2 sulfur atoms from thiocarboxylated Mocs2A into precursor Z to generate a dithiolene group. 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; composed of 2 small (Mocs2A) and 2 large (Mocs2B) subunits. This protein is produced by a bicistronic gene which also produces the small subunit (Mocs2A). Belongs to the MoaE family. MOCS2B subfamily.