Make your way to the Build Screener Survey step (#3 for public projects, #4 for private projects).
Under Start from an existing project, click Select... to see a menu of your team's current and past projects, including project name, project creator, and study type. (Draft projects won't show up in this list.) Pick the project whose screener you want to copy.
Copying a previous screener will erase any changes you've made to the blank screener in your new project, so double-check that you haven't started adding questions to your new project yet.
Once you've imported the screener into your new project, make any changes you want—edits won't affect the old project.