In brief, a new manager can always instantly see every performance review (even historic ones) of all people reporting to her either directly or indirectly. In addition, a manager can always see reviews she signed for previous team members (so no matter if the manager leaves the team, or the team member, the review is still accessible to the "old manager". Unless this manager leaves the company entirely of course).
Learn more about the details on the user management documentation.
The new manager will be able to edit an existing performance review in an open cycle. Before the new manager makes adjustments, the old manager's name will appear on the review. In order to have the new manager's name appear, they'll need to edit the review.