Classification of simple C*-algebras with unique traces

We classify certain almost multiplicative morphisms up to approximate unitary equivalence and use this result to prove the following: Let A and B be two unital separable simple C*-algebras of real rank zero, stable rank one, with weakly unperforated K₀-groups and with unique normalized quasi-traces. Suppose that both A and B are locally AH and (K_*(A),K_*(A)₊,[1_A]) ≅ (K_*(B),K_*(B)₊,[1_B]). Then A is isomorphic to B.