Cysteine synthase that can also catalyze the synthesis of S-sulfo-L-cysteine from thiosulfate and O(3)-acetyl-L-serine, as well as the sulfhydrylation of L-serine by sulfide. hydrogen sulfide + O-acetyl-L-serine = acetate + L-cysteine H(+) + hydrogen sulfide + O-phospho-L-serine = L-cysteine + phosphate L-homocysteine + L-serine = H2O + L,L-cystathionine Optimum pH is 6.7 for O-acetylserine sulfhydrylase A activity and 8.1-8.8 for cystathionine beta-synthase activity. Optimum temperature is above 90 degrees Celsius for S-sulfo-L-cysteine synthase activity, 70-80 degrees Celsius for O-acetylserine sulfhydrylase A activity, and 80 degrees Celsius for both cystathionine beta-synthase and L-serine sulfhdrylase activities. Amino-acid biosynthesis; L-cysteine biosynthesis; L-cysteine from L-serine: step 2/2. Homodimer. Belongs to the cysteine synthase/cystathionine beta-synthase family.