You have to assign the favicon yourself to the desktop shortcut (right-click the shortcut: Properties) after you have dragged the link to the desktop. You can usually find the favicon in Tools >Page Info > Media and save the icon there. Otherwise use the main domain of the website and add favicon.ico (e.g. mozilla.org/favicon.ico ) to display the favicon in a tab and save that image to a folder.

There's also this awesome add-on called Firefox Prism (which is discontinued afaik) and allows you to use webapps like desktop applications.

See https://addons.mozilla.org/en-us/firefox/addon/mozilla-labs-prism/

Tobbi, with all due respect, why even mention an add-on that hadn't been updated beyond Firefox 3.6 for a person using Firefox 9.0.1, and is discontinued??

I do not know where to find: You can usually find the favicon in

Tools >Page Info > Media and save the icon there.

I had tried that earlier b-4 posting my question and nothing...

Hit the Alt key to reveal the Menu Bar where the Tools menu resides.
You can also right-click the page and use the Page Info menu item.

Then click on the Media tab in the Page Info window.

it won't let me save the image in a format that the "browse" function will recognize. Right now the image is both gif & jpg. I KNOW that these aren't the right types but I can't save it as a dll or ico file. At least I don't know how... thanx as each suggestion is getting me closer!

Doesn't Vista have an All files selection in the drop-down to the right of Files of type in the Change Icon window?

If that doesn't help you, post a link to the page that you want to save the icon from so I can take a look at it.