migrate user sessions to cognito

Question

This is my first stack overflow question. I have an in-house written OAuth backend serving for my application. I have migrated all the users from my backend to Cognito using the user migration Lambda trigger. The problem is that they are a few other services that are already linked and are using the existing backend to authenticate and needed to be to migrate to Cognito without forcing them to log out and log in. is there a way? If yes, let me know. Thanks