Please see this support article to learn how the Firefox screenshot feature works:
https://support.mozilla.org/en-US/kb/firefox-screenshots

In short the user needs to save each screenshot as is is taken. There is no cache of saved screenshots.

I think I misrepresented my problem. What I mean is the background image in the "top sites" section. Not the screenshot that is taken manually.

Do you mean the thumbnails that Firefox can show in a tile on the Firefox Home page that sometimes show the first letter of that website and not a thumbnail that shows the view of the website ?

Yes. I want to know where the view of the website is stored at.

The thumbnails are stored in the thumbnails folder in the secondary Local Directory profile location that is also used for the disk cache.

Firefox uses two locations for the Firefox profile folder. Location used for the main profile that keeps your personal data (Root Directory on about:profiles).

• C:\Users\<user>\AppData\Roaming\Mozilla\Firefox\Profiles\<profile>\

Location used for the disk cache and other temporary files (Local Directory on about:profiles).

• C:\Users\<user>\AppData\Local\Mozilla\Firefox\Profiles\<profile>\

Thank you so much and have a great day.