Swap fork upstream/downstream relationship

Given an existing repo in an existing org, e.g. old-org/the-repo, I would like to create a new org with a fork of that repo e.g. new-org/the-repo, and then swap the upstream relationship so that new-org/the-repo is the upstream repo that old-org/the-repo tracks and has a “forked from” relationship with. I have admin access to both orgs.

Is this possible?