Homomorphisms into simple $\mathcal{Z}$-stable $C^*$-algebras, II

Let A and B be unital finite separable simple amenable C^* -algebras which satisfy the UCT, and B is \mathcal{Z} -stable. Following Gong, Lin, and Niu (2020), we show that two unital homomorphisms from A to B are approximately unitarily equivalent if and only if they induce the same element in KL(A,B) , the same affine map on tracial states, and the same Hausdorffified algebraic K_1 group homomorphism. A complete description of the range of the invariant for unital homomorphisms is also given.