Moodle let’s you do Migration in Place. That is: you toggle your tool from 1.1 to 1.3, fill in the required LTI 1.3 parameters and that’s it! All the data is still around.
But where did they go? In the id_token as openid or lti claims.
How to pass grade back? You now post score to the lineitem URL passed in the LTI message.
What about my consumer key? Well, you will have to prompt the user to do a rebinding of the Moodle issued client_id to the old consumer key.
All of this is covered in a Youtube presentation (LMS agnostic):