1. Add the Font Awesome font inside the extension folders
1.1. Go to Font Awesome and download it choosing the FOR THE WEB version.
1.2. Access the extension's files and folders and create a new folder, called "icons" or something similar.
1.3. Unzip the archive you downloaded from Font Awesome and copy the content of the folder inside the new "icons" folder.
2. Replace the Font Awesome CDN links with the version you have locally:
2.1.Find the Font Awesome CDN code inside the main .php file of the extension (usually named after the extension, for example mod_favcontent.php), for example:

Edit the above code and replace the FontAwesome CDN link, such as:
href="//use.fontawesome.com/releases/v5.1.0/css/all.css"
with:
href="https://yourwebsite.com/modules/extensionname/icons/css/all.css"