Involved in the synthesis of diacylglycerol galactolipids that are specifically found in thylakoid membranes. Specific for alpha-glycosidic linkages (PubMed:10381884, PubMed:14600212). Responsible for the final assembly of galactolipids in photosynthetic membranes. Digalactosyldiacylglycerol (DGDG) provides stability to the photosystem I (PSI) complex, especially to the PsaA, PsaB, PsaC, PsaL and PsaH subunits (PubMed:15961080, PubMed:16854937). a 1,2-diacyl-3-O-(beta-D-galactosyl)-sn-glycerol + UDP-alpha-D-galactose = 1,2-diacyl-3-O-[alpha-D-galactosyl-(1->6)-beta-D-galactosyl]-sn-glycerol + H(+) + UDP 6-fold up-regulation by phosphate deficiency. Altered thylakoid membrane lipid composition and stunted phenotype. Belongs to the glycosyltransferase group 1 family. Glycosyltransferase 4 subfamily.