If you drag a link or favicon on the left end of the location bar onto the desktop to create an internet shortcut then that shortcut gets the icon of the default browser.

If you want a different icon (favicon) then you have to assign that icon yourself to the desktop shortcut (right-click: Properties).

You can usually get the favicon if you append "favicon.ico" to the main domain of a website (e.g. http://www.mozilla.com/favicon.ico ) to display the favicon in a tab and save that image to a folder or see if you can find it in "Tools > Page Info > Media".

This workaround is not a solution. For example, MS Internet Explore will create the desktop shortcut with the correct site icon information included.

This should be a standard for Firefox also.

I have had to find the icon files for site icons, and they can be buried deep in imbedded code somewhere and difficult to find. This take time.

I believe since this is done in other browsers, that it can be done within Firefox.