Screen shot of how it looks?

Here's the screen shot. The original Firefox Icon is on the left and the Secondary Firefox Icon is on the right.

I would think something is a little mucked up in Firefox or in the registry. Suggest deleting the main icon with Firefox not running, Then do this :

• Repair System Registry and Files

Find the Dos Prompt Right or Powershell Click and Run as Administrator then : Copy/Paste to Dos Window : SFC /Scannow (SFC <space>/Scannow) then hit Enter. Reboot when completed.

Search for Firefox.exe and create a short cut and drag to the desktop or taskbar.

fyi: all the icons by the clock can be dragged to the upward pointing arrow and be stored there.

If that fails : uninstall Firefox. Then Delete the Mozilla Firefox Folders in C:\Program Files , C:\Program Files(x86) & C:\ProgramData Then restart system. Then run Windows Disk Cleanup. (Note: This should be Pinned and run Weekly, If never done below expect 10's of gig's) Then run it again and click the button that says Cleanup System Files. Note: your Firefox Profile is saved. But you should make a back up before you do :

• https://support.mozilla.org/en-US/kb/back-and-restore-information-firefox-profiles
• https://support.mozilla.org/en-US/kb/export-firefox-bookmarks-to-backup-or-transfer

Reinstall with Current Release Firefox 59.0.2 with a Full Version Installer

• https://www.mozilla.org/firefox/all/

Please let us know if this solved your issue or if need further assistance.

First I want to thank Pkshadow for the reply, but before I could effect the suggested fix,my computer did an automatic update and reboot over night; which for whatever reason, caused my Firefox Icon to disappear from my Taskbar. I replaced the shortcut to my Taskbar and now it's working correctly (only one Icon when a web page is open.) So as the saying goes, "If it ain't broken, don't fix it."

Again, please accept my sincere thanks for your assistance with this.