You can transfer quiz questions between modules, so long as you have editing teacher rights in both.
This refers to Moodle 2.7 from July 2015 onward
How to: transfer questions for quizzes between Moodle modules
Exporting the questions from a module
- Go into the module with the questions you want to export.
- Find the ADMINISTRATION block and click on Module administration > Question bank > Export
- Select the Moodle XML format
- Click on the Export questions to file button
- Your export file should start to download. If it doesn’t, click as indicated on the download page to download the file.
- Save the file to a folder on your hard drive (it may go into Downloads by default)
Importing the questions into another module
- Go into the module in Moodle into which you want the questions added.
- Find the ADMINISTRATION block and click on Module administration > Question bank > Import
- Select the Moodle XML format.
- Drag and drop the Question bank file you just downloaded into the box
- Click on Choose a file to load the file picker
- Click on Upload a file and then Browse for the file you downloaded earlier and click on Upload this file.
- Click the Import button
- Then click Continue to complete the process of importing the questions