I see answers to similar questions and I'm sure I may just not be familiar enough with Git and Github terminology to know if they apply to my question. What I need to do is to clone an existing Github remote repository (a private repo under another person's username that I have contributor access to) and create a new private remote repo under my account. The existing repo user is going to make significant alterations to the repo, delete, and re-push, before they do that they want me to clone and create a duplicate so we can continue working from the repo under my user. I want to preserve the commit history with the repo if possible.

I've cloned locally but don't can't seem to figure out how to push it to a new remote that isn't origined to the original user.