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, but not thiosulfate or thio-nitro-benzoate. O-acetylserine (OAS) is a very poor substrate in comparison with OPS. May be of particular importance for cysteine biosynthesis in the persistent phase of M.tuberculosis