This one says "save in your desktop in default":

Easy Screenshot 1.2.7.2 https://addons.mozilla.org/firefox/addon/easyscreenshot/

However, you seem to have another similarly named one --

Easy Screenshot (restartless) 0.1.5 https://addons.mozilla.org/firefox/addon/easy-screenshot/

-- so I'm not sure which one is actually doing the deed. If you don't see anything on your desktop, is there another folder where Firefox usually downloads by default?

Turns out it was right in front of my face, but I was busy trying to find it in another folder. I guess after it shot the screen, it appeared on my screen. Duh. But then someone told me I must have an old version of Firefox, but I just downloaded it FROM Firefox this morning.

Note that you do not really need an extension to take a full page screenshot because Firefox has this feature as part of built-in developer tools. Extensions likely use the same API to take the screenshot.

Firefox has a setting in the web developer toolbox settings to add a button to the toolbar of the Web Developer toolbox to take a full page screenshot.

• https://developer.mozilla.org/Tools/Tools_Toolbox#Settings
• Available Toolbox Buttons: Take a fullpage screenshot

The (default) file name is "Screen Shot yyyy-mm-dd at HH.MM.SS.png" and the file is saved to the Downloads folder. You can right-click and select "Inspect Element" to open the Inspector (Firefox/Tools > Web Developer) and have access to the developer tools including the cogwheel icon to access the toolbox settings and find the "Take a fullpage screenshot" (camera) button once you have enabled this button.

BelTstyles said

But then someone told me I must have an old version of Firefox, but I just downloaded it FROM Firefox this morning.

Sorry, but who told you that? Your Firefox reported itself as the current version when you posted (Question Details to the right of your question), so anyone familiar with how to use this forum would know you're up-to-date.