Transfers at FCO are beyond easy!

You'll arrive at T3. From there you'll walk through the terminal to the tram. You'll take it to the first stop which will be T1 and the B gates which is more than likely were your connecting flight will depart from. There will be a small security station here that you'll go through. Very quick and easy. From there you'll head through T1 to the B gates. This can be a little confusing, but just keep an eye for the signs and you'll be fine.

About halfway through (or at least that's how it felt to me) you'll come to passport control. They'll take a quick look at your passport and BP and you'll be on your way. From there it is a short walk to the gates. Don't stress it - easiest transfer of my life!

everything happens air side. You won't have to leave the terminals etc. As long as you follow the signs, it will be a piece of cake. I managed to do and I had 30 mins to catch my connecting flight.