Specifically catalyzes the beta-elimination of phosphate from L-phosphoserine and the beta-addition of sulfite to the dehydroalanine intermediate to produce L-cysteate. Does not display threonine synthase activity like the paralog protein ThrC. H(+) + O-phospho-L-serine + sulfite = L-cysteate + phosphate Is inhibited by AP3 (DL-2-amino-3-phosphonopropionate) and, to a lesser extent, by L-aspartate or AP4 (DL-2-amino-4-phosphonobutyrate). Is also inhibited by EDTA in vitro. Cofactor biosynthesis; coenzyme M biosynthesis. Homotrimer. Belongs to the threonine synthase family. Cysteate synthase subfamily.