You can transfer any project you own to another user or organization. For example, a project that started out as a private scratch workspace can be shared with colleagues by transferring ownership to your organization. To do this, (1) go to the project’s settings page, (2) choose the "Archive Project or Transfer Ownership" tab, and (3) click the “Change Project Owner” on the right side. A pop up will show where you can enter the new owner’s user or organization name.
After ownership is transferred, the new owner will receive an email notifying them of the change. Organizations do not receive emails.
If you were using an API endpoint in the original project, it will stop serving requests after ownership transfer. The new owner can re-publish it for further use, but note that the endpoint URL will change and your API key will no longer work (unless you are given Contributor access). So be sure to re-point any external system that calls it, and to coordinate around the downtime.
To avoid downtime, you can instead follow these steps:
Have the new owner fork the project (you will need to give them access as a Contributor or Results Consumer.
Re-publish the endpoint in the new project.
Point your system to the new URL.
Shut down the original endpoint (and archive the original project, if you like).