Firefox has nothing to do with Chrome or Google account. And since nothing was provided so others can back track what happened or what Chrome support said it's up to anybody what was said. And also you don't need a Firefox account to use the Browser that is mainly for the forum and sync one Firefox to another Firefox. So not sure what Chrome or Google relates to Firefox as no one was there during the install to see what was going on there. Also not sure what is meant by this as well:

I tried to use my desktop shortcuts ?????

And also you don't need a Firefox account to use the Browser that is mainly for the forum and sync one Firefox to another Firefox.

It syncs to a sync server and not device to device as you still think it is.

The Firefox Account is used for multiple Mozilla services besides for Sync and SUMO as you can see on https://support.mozilla.org/en-US/kb/access-mozilla-services-firefox-account

James, in all respect, I think you did not understand my problem. I appreciate your taking the time to reply to my question, but there's nothing in your reply that addresses the problem I experienced after installing the Firefox browser.

Prior to installing I never had a problem with sync using Chrome. I never had a problem with shortcuts to Chrome, Gmail and Photos not working.

So, something happened when I installed Firefox, and did the sync to bring over passwords, history, etc from Chrome.

I had no problems with sync in MS Edge, it sync'd just fine with Google Chrome.

I'm not a tech expert, just a user with a good deal of experience. I've installed Edge and Chrome browsers and never had anything like this happen. So give this some more thought and see if you or your associates can tell me why this occurred and help make sure it doesn't happen again if I choose to reinstall Firefox.

Thanks for the help

Ken