As a business requirement, we have a website (https://www.123.com) which is integrated with SSO (thru SAML). The authentication on this site is IDP initiated. On the other hand, I have another website (https://www.231.com) which is also integrated with SSO but authenticated is SP initiated. How can we share a user session between the websites. Meaning if I logged in at https://www.231.com, I don't want the user to click to log in on the https://www.123.com to show them a logged-in user.
You would need to share the cookies between both domains, which is hardly possible due to browser restrictions. You will require at least one time the user to click login again (even if the user doesn't have to enter the credentials again).