Hi, it should do!

Go to Start Menu > All Programs, then right click on Mozilla Firefox, Send to Desktop > Create Shortcut. (That might not be the exact wording because I'm using Win10 which is different).

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No. Only sends shortcut to Firefox, not to website.

Ah it's a website shortcut you want! Please see; Create a desktop shortcut to a website

Are you talking about the Firefox logo and not the website Favicon image appearing for the desktop shortcut?

If so, Microsoft does that with any 3rd party browser. Only IE is allowed to place the website image with the desktop shortcut automatically. Although the user can save the image them self and then Change icon thru Properties for that shortcut. A lot of work, IMO, for little "value".