Adding an administrator to a Facebook business page
To add an administrator of your Facebook business page you, first of all, have to be an admin yourself!
If you are, simply follow these steps:
1. Click on "Settings" located at the top right of your business page.
2. Choose "Page Roles" from the menu of options located on the right-hand side of your screen
3. Enter the email address connected to your new admin's Facebook profile and choose which role you would like to assign them from the dropdown (screenshot below).
There are several roles to choose from: Admin, Editor, Moderator, Advertiser, and Analyst.
NOTE - to see detailed information on what each role can do please select the role from the dropdown and note the description beneath the role title.
4. Once you have selected the role click "Add" and you are done!
For more information on Roles within a Facebook Business Page please use this Facebook Help article.