When we first started using Asana, we setup a private project to manage some of our team’s tasked. We now want to move that private project into a separate team (with the same members) but don’t see that as an option for any of the private projects.
I believe you will need to ensure you have access to the project, be a member of the source team in which it is currently found, and be a member of the destination team into which you want to move it.
If you don’t have the ability to be part of both teams, which is a case I encountered, you can create a 3rd team as a “proxy” to pass the project to someone from the target team, and let pull it in their team