You can import questions from a quiz in Brightspace to the question library in Brightspace.
Go to the Quizzes tab and select Question Library. Create a New section, from the dropdown menu. In this way, a new folder/quiz section will be created and named. Click on save and continue to the new section that you just created. Select Import and choose Browse Existing Questions from the dropdown menu. A popup will open on your right. Select Source and choose the name of the quiz you want to be imported. Now, you can select the questions to be added by clicking Add. When finished, select Done Editing Questions.
You can also follow the instructions in this short video: