Reversibly phosphorolyzes beta-D-galactopyranosyl-(1->3)-N-acetyl-D-glucosamine to form alpha-D-galactopyranose 1-phosphate and acetyl-D-glucosamine. Active towards galacto-N-biose and lacto-N-biose. Does not phosphorolyze galacto-N-tetraose or lacto-N-tetraose. In the reverse reaction has activity toward N-acetyl-D-glucosamine and N-acetyl-D-galactosamine, but not L-rhamnose, D-glucose or D-galactose. beta-D-galactosyl-(1->3)-N-acetyl-D-glucosamine + phosphate = alpha-D-galactose 1-phosphate + N-acetyl-D-glucosamine Belongs to the glycoside hydrolase 112 family.