A single Quiz activity cannot be exported/imported between two Moodle courses.
The best way to duplicate a quiz into another Moodle course is to export the questions for that quiz. Then, import the questions into the second course and re-create the quiz activity manually.
For this process to work correctly, the questions should all be in one Category in the Question Bank of the source Moodle course.
1. Click on the Quiz:
2. In the Contextual menu at the top, find and select Question bank.
3. Above the Question Bank heading, look for a drop-down box and find Export from the list.
4. Select the Moodle XML format.
5. Under the General heading, select the Category containing the questions for export.
6. Click the Export questions to file button. A file will be downloaded onto your computer. It cannot be opened.
7. Go into the second Moodle course and import these questions, making sure to select Moodle XML as the question format.
8. Lastly, create a new Quiz activity in the second Moodle course and add the imported questions into it.
Return to the Quiz main resource page for more information on other topics.