Dynamical Systems Implemented by Isomorphic Groups of Unitaries

Let $\varphi:A\to B$ be an isomorphism of $C^*$-algebras and $I$ be an ideal of $A.$  Introducing the concepts of unitary equivalent and the implemented Finsler modules, we show that the $\frac{A}{I}$-module $\frac{E}{E_{I}}$ and the implemented  $\frac{B}{\varphi(I)}$-module  $\frac{F}{F_{\varphi(I)}}$  are unitary equivalent. We also,  establish a one to one correspondence between  the groups $U(E)$ and $U(F)$ of  unitaries on full Finsler modules $E$ and $F,$ respectively.   Finally, we explain regularized  dynamical systems and   apply the aforementioned one to one correspondence to prove that  each regularized  dynamical system in $U(E)$ implements a regularized  dynamical system  in $U(F).$