Catalysis of the reaction: 2 mono-beta-D-galactosyldiacylglycerol = acylmono-beta-D-galactosyl-diacylglycerol + mono-beta-D-galactosylacylglycerol.
mono-beta-D-galactosyldiacylglycerol:mono-beta-D-galactosyldiacylglycerol acyltransferase activity