Hi Andrei

Once a quiz has been attempted then you won't be able to change the questions in the quiz as this will lead to inconsistent results.

To retain the results from the previous quiz the safest way is to add a new quiz and hide  the old quiz through access restrictions  maybe through date or non completion of the old quiz.

If the course completion conditions included the criteria that the old quiz activity needs to be completed then you would need to unlock the activity completion criteria and add the new quiz as an course completion criteria . T

The setting that is probably suited to your case is 

Unlock completion and keep completion data: Keep all existing completion records and accept that different users may have received their status for different accomplishments.

This will mean that any users who have completed the course with the old quiz will still have their completion record retained.

Have a test of this to see that this does what you want.

Regards