Authentication only from external website

We have an existing php website (not using Auth0) and we would like some of our users to have SSO access to another company’s website using Auth0. So users must first log into our website as normal and then click a link to the external website without having to log in there too. The other company is using Auth0.

How can I set this up without modifying our current login process? Can it be done easily with Auth0 or should I set up a SAML identity provider on our website? Thank you.