Hello. If this is what I think it is then,
the procedure depends on shortcut file extension.
If you can't see shortcut file extension then here is how to enable this:
Press Windows key + R and type or copy paste bellow string and hit enter:
control.exe folders
in file explorer options click on "View" tab
then make sure "Hide extensions for known file types" is not checked
Now on your desktop check file extensions for these shortcuts.
If you still can't see the extension then the extension is *.url
Click on Start button and open Settings app
Click on Apps
Click on Default apps
Scroll down and click on "Set default apps by file type"
Now in that long list find the extension that those shortcuts use.
then if next to file extension there is + (plus) sign click on it and select Firefox browser or just internet browser or locate firefox.
If next to extension is something else but not firefox, set it to firefox.
That's it, this should show the icons,
however if extension type is *.url, shortcut icon may depend on contents of that file.
so you can try to recreate this shortcut.
If unsure what is the actual url, open the shortcut with notepad, and there is url you need, visit this url,
and make a new shortcut or bookmark
the procedure depends on shortcut file extension.
If you can't see shortcut file extension then here is how to enable this:
Press Windows key + R and type or copy paste bellow string and hit enter:
control.exe folders
in file explorer options click on "View" tab
then make sure "Hide extensions for known file types" is not checked
Now on your desktop check file extensions for these shortcuts.
If you still can't see the extension then the extension is *.url
Click on Start button and open Settings app
Click on Apps
Click on Default apps
Scroll down and click on "Set default apps by file type"
Now in that long list find the extension that those shortcuts use.
then if next to file extension there is + (plus) sign click on it and select Firefox browser or just internet browser or locate firefox.
If next to extension is something else but not firefox, set it to firefox.
That's it, this should show the icons,
however if extension type is *.url, shortcut icon may depend on contents of that file.
so you can try to recreate this shortcut.
If unsure what is the actual url, open the shortcut with notepad, and there is url you need, visit this url,
and make a new shortcut or bookmark