Allowing my customer's users into my Cognito-authentication-based LMS

I've developed several native Android and IOS apps as well as a Wordpress LMS that employ a Cognito authentication environment that's working very well authenticating tens of thousands of users with accounts in a single user pool.

Now I have an external customer that wants to provide access to my organization's LMS courses to their users. Their users are authenticated in their portal, and they do not want their users to have to login to my environment or maintain credentials in my environment. They just want to provide a link to my courses in their portal and then allow their users to seamlessly access these courses.

I know there's got to be a way to do that (to have my Cognito environment trust their environment to authenticate their users) using something like Cognito Federated Identities and SAML configuration (or some similar combination) but I'm getting lost understanding first the high-level design of such a solution and then of course the particular implementation.

Thank you in advance for any guidance you may give!