I am reading a paper by David Blecher, which contains the following:

" If $T: Y \to Z$ is a surjective isometric module map between $W^{*}$-modules over $M$, then $T$ is unitary. Also, $T$ is a $w^{*}$-homeomorphism, and the unique preduals of $Y$ and $Z$ are completely isometrically isomorphic via the module map $T_{*}$."

I have no problem with the unitary part. Also, I know that if $T$ is $w^{*}$-continuous then it is a $w^{*}$-homeomorphism. What I don't get is why do we know $T$ is $w^{*}$-continuous?

Since this statement is given without proof, it makes me think that this is a well known fact. I"ll appreciate any explanation or reference to a proof of this.