How can static method access class variable in Python?

You can access it as InviteManager.INVITE_MESSAGE, but a cleaner solution is to change the static method to a class method:

@classmethod
@missing_input_not_allowed
def invite(cls, email):
    return cls.INVITE_MESSAGE

(Or, if your code is really as simple as it looks, you can replace the whole class with a bunch of functions and constants in a module. Modules are namespaces.)