Synthesizes the galactose-alpha(1,3)-galactose group by catalyzing the transfer of a galactose residue, with an alpha-1,3 linkage, on terminal lactosaminide (Gal-beta-1,4-GlcNAc-R) disaccharide borne by a glycoprotein or a glycolipid. Preferentially glycosylates proteins, can synthesize galactose-alpha(1,3)-galactose on glycoproteins but cannot synthesize the glycolipid called isogloboside 3 (iGb3) (By similarity). a beta-D-galactosyl-(1->4)-N-acetyl-beta-D-glucosaminyl derivative + UDP-alpha-D-galactose = an alpha-D-galactosyl-(1->3)-beta-D-galactosyl-(1->4)-N-acetyl-beta-D-glucosaminyl derivative + H(+) + UDP Binds 1 Mn(2+) ion per subunit. Protein modification; protein glycosylation. Membrane-bound form in trans cisternae of Golgi. The conserved DXD motif is involved in cofactor binding. The manganese ion interacts with the beta-phosphate group of UDP and may also have a role in catalysis. Belongs to the glycosyltransferase 6 family.