Retroactively Awarding Extra Exam Time

You don't have to be the person who decides what to do in this situation. Actually, there are many reasons to remove yourself from making further decisions. Take it back to the administration of your Department / University, give them a fair account of what's happened, and let them decide what to do.

Dmitry's suggestion is an excellent one. I would like to offer another. You can explain the situation to the student and offer a few compensation options. It can be boosting grades in ratio of the lost time or another exam of similar difficulty. I fear an administrative decision might yield a negative result for the student. As far as I am concerned, the student should not be in a disadvantage when it is not their fault.