Catalyzes the conversion of O-succinyl-L-serine into cysteine, the last step in the cysteine biosynthesis pathway. Can also use O-acetyl-L-serine. hydrogen sulfide + O-succinyl-L-serine = L-cysteine + succinate hydrogen sulfide + O-acetyl-L-serine = acetate + L-cysteine Amino-acid biosynthesis; L-cysteine biosynthesis; L-cysteine from L-serine: step 2/2. Belongs to the cysteine synthase/cystathionine beta-synthase family.