  Motivated by understanding the Brou\'e's abelian defect group conjecture from
algebraic point of view, we consider the question of how to lift a stable
equivalence of Morita type between arbitrary finite dimensional algebras to a
derived equivalence. In this paper, we present a machinery to solve this
question for a class of stable equivalences of Morita type. In particular, we
show that every stable equivalence of Morita type between Frobenius-finite
algebras over an algebraically closed field can be lifted to a derived
equivalence. %Thus Frobenius-finite algebras share many common %invariants of
both derived equivalences and stable equivalences. Especially, Auslander-Reiten
conjecrure is true for stable equivalences of Morita type between
Frobenius-finite algebras without semisimple direct summands. Examples of such
a class of algebras are abundant, including Auslander algebras, cluster-tilted
algebras and certain Frobenius extensions. As a byproduct of our methods, we
further show that, for a Nakayama-stable idempotent element $e$ in an algebra
$A$ over an arbitrary field, each tilting complex over $eAe$ can be extended to
a tilting complex over $A$ that induces an almost $\nu$-stable derived
equivalence studied in the first paper of this series. Moreover, we demonstrate
that our techniques are applicable to verify the Brou\'{e}'s abelian defect
group conjecture for several cases mentioned by Okuyama.
