As Hightech pointed out, you can import the test cases from one project to another but only if you're using the server app.
If you're using the cloud app, you'd have to export the test cases and then import them into the project you want.
In the source project, select the test cases you want to move, click on the More ▾ button, and then Export to XML;
In the target project, click on the ellipsis (...) button next to the + New button, and then Import from file. Select Zephyr Scale as the data source and upload the file you've just downloaded. Follow the instructions on the screen to finish the import.
Test cases and folders are created automatically, but if you have custom fields, custom status, and custom priorities, you'll have to create them again in the target project.