How to use WP Fastest Cache with Protected Password Plugin?

Hello,

The context:

Let’s say we have a WordPress site in the customers.mywebpage.com where they can login with only a password (not a user wordpress login).

We are using that Plugin:
https://es.wordpress.org/plugins/password-protected/

That makes the all site private, you can see the website only if you have a unique password. Supose the password is “Onlyforcustomers”.

The issue:

In this context, WP Fastest Cache cannot Preload the pages, because cannot enter to the website. So it doesn’t work with the Plugin Password Protected.

The question:

Is there a way to make WP Fastest Cache works with this Plugins in this context? If not, is there any other alterantive to make website fully private with a unique password where WP Fastest Cache can preload all pages?

Thanks