As someone who has created several pages on Facebook for clients, I noticed that when I create the page, I’m the one admin that can’t be removed. That can be a problem if the relationship between you and your client ends.
This article by Social Media Today discusses the dilemma and offers one solution, although not the ideal solution.
My suggestion is that you secure your client’s Facebook log in info and log in as your client, creating the page from their account. Make sure you’re one of their friends, or “likes” and you can add yourself as an Admin. That way, if down the road you part ways, they maintain ownership of the page as the creator.