  We construct two functors from the submodule category of a self-injective
representation-finite algebra $\Lambda$ to the module category of the stable
Auslander algebra of $\Lambda$. These functors factor through the module
category of the Auslander algebra of $\Lambda$. Moreover they induce
equivalences from the quotient categories of the submodule category modulo
their respective kernels and said kernels have finitely many indecomposable
objects up to isomorphism. Their construction uses a recollement of the module
category of the Auslander algebra induced by an idempotent and this recollement
determines a characteristic tilting and cotilting module. If $\Lambda$ is taken
to be a Nakayama algebra, then said tilting and cotilting module is a
characteristic tilting module of a quasi-hereditary structure on the Auslander
algebra. We prove that the self-injective Nakayama algebras are the only
algebras with this property.
