Catalyzes the formation of a covalent CysO-cysteine adduct via a sulfur transfer, using the thiocarboxylated sulfur carrier protein CysO-COSH as sulfur donor and O-phospho-L-serine (OPS) as sulfur acceptor. Can also use sodium sulfide as sulfur donor in vitro, albeit with less efficiency. [CysO sulfur-carrier protein]-Gly-NH-CH2-C(O)SH + O-phospho-L-serine = [CysO sulfur-carrier protein]-Gly-NH-CH2-C(O)-S-L-Cys + phosphate Amino-acid biosynthesis; L-cysteine biosynthesis. Homodimer. The five C-terminal amino acid residues are inserted into the active site cleft in the closed conformation, protect the aminoacrylate intermediate and are involved in sulfur donor selectivity. Belongs to the cysteine synthase/cystathionine beta-synthase family.