a 6-O-sulfo-N-acetyl-beta-D-glucosaminyl-(1->3)-beta-D-galactosyl-(1->4)-N-acetyl-beta-D-glucosaminyl derivative + UDP-alpha-D-galactose = a beta-D-galactosyl-(1->4)-6-O-sulfo-N-acetyl-beta-D-glucosaminyl-(1->3)-beta-D-galactosyl-(1->4)-N-acetyl-beta-D-glucosaminyl derivative + UDP + H(+) — reaction