Catalysis of the reaction: 1,2,3,6-tetrakis-O-galloyl-beta-D-glucose + 1-O-galloyl-beta-D-glucose = 1,2,3,4,6-pentakis-O-galloyl-beta-D-glucose + D-glucose.
beta-glucogallin:1,2,3,6-tetra-O-galloylglucose 4-O-galloyltransferase activity