Web: Redirecting to a webpage with data(not as URL or query params)

I have a webapp, say, example1.com and the user logged into it. I have the user data in my localStorage. After a particular event, say, button click, I want to redirect the user to example2.com with the user data from localStorage. But the user data shouldn't be sent as url or query params. It shouldn't be visible to the enduser at all.

What are the ways we can achieve this ?