Transfers a succinyl group from succinyl-CoA to L-serine, forming succinyl-L-serine. Has also weak serine acetyl transferase activity and homoserine succinyl transferase activity. L-serine + succinyl-CoA = CoA + O-succinyl-L-serine kcat is 7.4 sec(-1) with L-serine and succinyl-CoA as substrates. kcat is 0.2 sec(-1) with acetyl-CoA as substrate (in the presence of L-serine). kcat is 13.8 sec(-1) with L-homoserine as substrate (in the presence of succinyl-CoA). Amino-acid biosynthesis; L-cysteine biosynthesis; L-cysteine from L-serine: step 1/2. Belongs to the AB hydrolase superfamily. MetX family.