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.
2.1.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"