I have a Facebook account and I want other people to use it as well. (Of course this is not my personal one, just an account for work.) However, when I share it, Facebook constantly alarms me about being hacked, even forcing me to change my password. How to tell it that I know that already?
First thing, you should not share your Facebook password with anyone else. It's a violation of Facebook’s Statement of Rights and Responsibilities to share or solicit a Facebook password.
not share your password, give access to your Facebook account to others or transfer your account to anyone else (without our permission).
So, if you are sharing it with anyone, let Facebook send you the security email alert. Because whenever your account get logged-in from new device or browser, Facebook send an email alert to registered email-id. If they come to know that you are violating any policy, they will suspend or disable your account.
So, for safe side if you are getting email alert, you can click on that link (if given) which ask if it's you are not. Or simply ignore those mails.