Show page in menu only when password has been entered

Hi, I’m wondering how I would show a password protected page in the menu bar of my website, but ONLY once the password has already been entered?

I am using a plugin called Smart Passworded Pages which basically lets the customers enter in a password they have been given, and it takes them to the password protected page with the matching password. Here is the plugin for reference: https://www.ads-software.com/plugins/smart-passworded-pages/

What I would like to achieve, is when the password has been registered for the password protected page, the page link would then appear in the menu bar so that the customer could easily navigate back without having to enter the password all over again.

Many thanks.