Involved in the synthesis of diacylglycerol galactolipids that are specifically found in thylakoid membranes. Specific for alpha-glycosidic linkages (PubMed:11696551, PubMed:14600212). During phosphate shortage, involved in the biosynthesis of digalactosyldiacylglycerol (DGDG) which rescues the limitation of phospholipids (Probable). 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 Stimulated by anionic phospholipids. Expressed in leaves, flowers and roots, but not in stems and siliques. 30-fold up-regulation by phosphate deficiency. No visible phenotype under normal growth conditions. Belongs to the glycosyltransferase group 1 family. Glycosyltransferase 4 subfamily.