That is an add that Microsoft sends.

Go to the Mozilla Add-ons Web Page {web Link} (There’s a lot of good stuff here) and search for a good ad blocker.

I have the latest microsoft chrome already on my desktop but Firefox keeps asking me to download it, Can it not register that I alreeady have this?

Is your homepage a Microsoft website like say their Bing.com search engine site? as they do prompts to get you to download Edge on some of their Microsoft sites if you are not using Edge.