Is "something is passed to someone" correct? Or should it be "something has been passed to someone"?

They are simply different tenses of "to be passed"

The instruction book has been passed to her for her perusal

Someone had the book and they passed it to her. This has happened recently and presumably she still has the book.

The instruction book is passed to her for her perusal

This either acts as a commentary, as for a sporting event, or it describes a regular occurrence, e.g.

Every day, as she enters the library, the book is passed to her for her perusal. We presume that, as she leaves the library, she passes it back.