Is there any plugin that allow me to set up the website in this way?
User A of a WordPress-based website can view only the post #1.
User B can view only posts #2 and #3.
User C can view only posts #1 and #3.
User D can view all posts.
Every user is registered manually by the admin, who will provide the username and password to the client and will select manually the post every user can view.
Thank you.
Pretty sure something like This will do what you need.