  Let $k$ be an algebraically closed field. It is known that any stable
equivalence between standard representation-finite self-injective $k$-algebras
(without block of Loewy length 2) lifts to a standard derived equivalence, in
particular, it is of Morita type. We show that the same holds for any stable
equivalence between nonstandard representation-finite self-injective
$k$-algebras. We also fill a gap in the original proof in standard case. This
gives a complete solution of the liftability question raised by H. Asashiba
about twenty years ago.
