Hydro-lyase catalyzing the first step of the transsulfuration pathway, where the hydroxyl group of L-serine is displaced by L-homocysteine in a beta-replacement reaction to form L-cystathionine, the precursor of L-cysteine. L-homocysteine + L-serine = H2O + L,L-cystathionine Has no response to S-adenosyl-methionine/AdoMet, unlike mammalian orthologs (PubMed:29275181). Binds non-covalently to a heme group that may control the redox sensitivity of the enzyme (By similarity). Amino-acid biosynthesis; L-cysteine biosynthesis; L-cysteine from L-homocysteine and L-serine: step 1/2. Homodimer. Belongs to the cysteine synthase/cystathionine beta-synthase family.