If you use SHARE/iTUNES and there is already a Media Browser copy, it should be very fast, because it does not have to render again.
The physical media browser files are stored in the project.
Go to your Movies/iMovie Projects folder in the Finder and you should see your projects.
Right-click on a project and select SHOW PACKAGE CONTENTS. There should be a folder in the package called MOVIES. That is where the Media Browser copies are. Be careful not to change anything within the package so you do not cause corruption in your project, but copying movies from the Media Browser should be OK. You will need to name them as well, because the Media Browser copies have generic names based on size.