I wonder why there is a second installation at all. Did anything weird happen during a recent update? Have you had house guests who might have done that? You might want to run some malware scans at some point. This article lists tools other Firefox users have found helpful: Troubleshoot Firefox issues caused by malware.

Cleaning up the unwanted installation

When you open the Properties dialog to the Shortcut tab, there is an "Open File Location" button. That will take you to the specific installation. You can use that to get to the unwanted folder(s) and delete them. Then get rid of that shortcut.

Next Steps

In case Firefox used that alternate location due to a permissions/privileges problem, I suggest doing a normal shutdown and restart of Windows before reinstalling.

Then see whether your regular Firefox needs to update and whether the update installs where it should: Update Firefox to the latest release.

If that goes into the wrong location, repeat the deletion of the unwanted folders, then, to ensure that the next time you install Firefox it installs in a sensible location, check out the steps in this article using the full installer: Custom installation of Firefox on Windows.

As for cleaning up the Windows control panel, hopefully the installer will do that automatically so you don't need to go poking around in the registry.

Thank you for your help.

I have been installing programs on my new laptop. I think I accidentally clicked on the firefox after I had already installed firefox.

The firefox app that was shown as an installed app and for which the target is Desktop Icon Target "C:\Program Files\Mozilla Firefox\firefox.exe" was showing as still active in Task Manager. I end tasked it and was able to remove using the W11 app installer as is done for other installed programs.

I still have installed the firefox from the second install. It is in the Target path "C:\Users\FEDER\AppData\Local\Mozilla Firefox\firefox.exe". It does not show as an installed app in W11.

Are you saying I can go to folder for firefox in the path C:\Users\FEDER\AppData\Local\Mozilla Firefox\ and delete folder Mozilla Firefox? If I do delete, do I need to delete registry entries for firefox since firefox no longer on my laptop?

Are you saying I can go to folder for firefox in the path C:\Users\FEDER\AppData\Local\Mozilla Firefox\ and delete folder Mozilla Firefox?

Yes, I don't see why not. You don't want it, so, let's get rid of it.

If I do delete, do I need to delete registry entries for firefox since firefox no longer on my laptop?

I wouldn't bother. If you run a custom install on your next installation, pointing to the desired folder, then the installer should update those entries if needed.