First of all, you'll have to "copy" your existing live site to the newly created offline WAMP environment.

You have two options here. You can use a plugin that will do the heavy lifting for you, or you can move your files manually. Obviously, doing it manually is harder and involves some coding, so I won't waste your time with that option.

OK. So let's see the magic ...

First you need to install a free plugin called WP Clone.

Here's the link:

https://wordpress.org/plugins/wp-clone-by-wp-academy/

A few words about this great plugin ... There are (too) many cloning plugins out there, but in my opinion WP Clone is the easiest, fastest and most secure way to ...

• move or copy a WordPress site to another domain or hosting server
  
• move your site to/from local server hosting
• create copies of your site for development or testing purposes
• backup your site
• install pre-configured versions of WordPress

Why? Because ...

• doesn't require FTP access to either the source or destination site
• it does not backup or restore the WordPress system files (just the user content and database), reducing the upload time and improving the security of your site
• it fetches the site backup via your host's direct HTTP connection, which saves you from needing to upload large files through your internet connection

With that having said, let's see the magic!