The easiest way to do this is to export the quiz, then re-import it back into your course. This will add all questions from the quiz to a question bank so you may end up with some duplicates but you can delete any unwanted duplicate questions from the bank once the import is complete.
This is a topic that is discussed quite frequently, so take a look at this recent discussion for more details on how it's done:
Would be greatly improved if you could just check boxes of quiz questions and then choose to insert them into a bank. In the bank, where it says, "Add a question," you should have option of adding questions from already-made quizzes. Plus, the question banks don't sync with changes made in the quiz questions (and vice versa). That's a problem too. That means one's final version of the quiz question never enters the bank. So, if I use this question on a review exam or final exam, the students are being treated unfairly since the bank question differs from the one I gave them originally. Some significant improvement is needed on banks. Allow easy selection from quizzes to banks and have quiz-question changes sync with the question in the bank. These are suggestions that hope development takes into consideration.
Were you able to find an answer to your question? I am going to go ahead and mark this question as answered because there hasn't been any more activity in a while so I assume that you have the information that you need. If you still have a question about this or if you have information that you would like to share with the community, by all means, please do come back and leave a comment.