If you are friends with this person on Facebook you can go into your Page Settings and edit Page Roles. Assign them the role you wish, depending on what you want them to be able to do. They will then have access to the Page. In your case I would assume you would assign whoever as an Editor. If you're on your desktop and doing this, Facebook will give you a layout of who can do what in different Page Roles -- you will see link at top of page when you hit Page Roles under Settings.