Hydrolyzes kojibiose in the presence of an inorganic phosphoric acid to form D-glucose and beta-D-glucose-1-phosphoric acid. Can act with alpha-1,2-oligoglucans, such as selaginose, as substrate, but more slowly. Inactive when disaccharides with linkages other than alpha-1,2 linkages, such as sophorose, trehalose, neotrehalose, nigerose, laminaribiose, maltose, cellobiose, isomaltose, gentiobiose, sucrose and lactose, are used as substrates. kojibiose + phosphate = beta-D-glucose 1-phosphate + D-glucose Optimum pH is 5.5. Optimum temperature is about 65 degrees Celsius. Belongs to the glycosyl hydrolase 65 family.