Catalysis of the reaction: (n) = (n-1) + alpha-D-fructofuranose beta-D-fructofuranose 1,2':2,3'-dianhydride. This reaction is the production of alpha-D-fructofuranose beta-D-fructofuranose 1,2':2,3'-dianhydride (DFA III) by successively eliminating the diminishing (2->1)-beta-D-fructan (inulin) chain from the terminal D-fructosyl-D-fructosyl disaccharide.
inulin fructotransferase (DFA-III-producing) activity