Once the A/B test has initially run for the user, the allocated variant of the A/B test will be associated with that user's browser.
This means that going forward this browser will not switch between the A/B test variants, and will remain in the same A/B test group until the test has ended, or until the A/B test proportions have been modified.
So in case, you'd change the offer in one of the branches, it will not have an impact on a current active test - a new offer will be shown to users allocated to the updated variant/s.