Specifically catalyzes the beta-elimination of phosphate from L-phosphoserine and the beta-addition of sulfite to the dehydroalanine intermediate to produce L-cysteate. H(+) + O-phospho-L-serine + sulfite = L-cysteate + phosphate Cofactor biosynthesis; coenzyme M biosynthesis. Homotrimer. Belongs to the threonine synthase family. Cysteate synthase subfamily.