How to share auth between my hosted website and firebase?

I am developing a website and a chrome extension. The website uses firebase authentication such as Facebook, Google, and Email. I making a chrome extension and need to share auth with it, meaning once users sign in to my website they also are logged in chrome extension. Is it possible to do that? I have already integrated firebase authentication within my chrome-extension and website separately. I am looking for a way to share auth. Thanks and Regards,