IS THE DURATION OF TIME ENOUGH TO TRANSIT?

My flight arrives at T2 at 22.25hrs. I have to take an international flight from T3 at 1.55hrs. By the time I arrive at T2 and collect my baggage it will be around 23.00hrs. I read here that from 23.00hrs onwards the cross terminal shuttle bus service is only available every 30 minutes. Do you think I have enough time to go to T3 and complete the transit procedures for my flight on time? In all, I have 3hrs and 30 minutes between the two flights. Thank you in advance