Let $X$ be a complex manifold. Denote by Div$(X)$ the Weil divisors group of $X$.
We have to:
Let $f : X \longrightarrow Y$ be a holomorphic map of connected complex manifolds and suppose that $f$ is dominant, i.e. $f(X)$ is dense in $Y$. Then the pull-back defines a group homomorphism $$ f^* :Div(Y) \longrightarrow Div(X). $$
Question: If $f : X \longrightarrow Y$ is an analytic isomorphism ( bi-holomorphic map), then is it true that $f^*:Div(Y)\longrightarrow Div(X)$ is a group isomorphism?