Corollary 1

Let A and B be Morita equivalent $k$-algebras, and let P be an invertible $(A,B)_k$-bimodule. There exists an isomorphism $\varphi$ from the center Z(A) of A to the center of B determined by the relation $\varphi (z)_P=z_P$ for every $z\in Z(A)$. The automorphisms of the $(A,B)_k$-bimodule P are the homotheties $z_P$ where $z$ is an invertible element of Z(A).

Given Theorem 1, this follows from Remark 2 of VIII, p. 97.