To add another account with admin rights to your salon's Facebook page, you must first add that person as a friend.
Once they have accepted, go to the settings for you page - this can be accessed by clicking 'Settings' on the top right of your page
From here you need to choose 'Page roles'
Here you can add people as admins which will allow them to manage the page using the 'Assign a new page role' section
Search for the person you are looking to add
Change the role from Editor to Admin
and click 'Add'!