I'm not sure - it's tricky and the suica app is all in japanese... with the time change right now I didn't want to bother my wife with trying to sort it out remotely and I had to get my new phone set up ahead of heading back to Japan next week.

What I did was transfer my phone's suica in apple pay to my apple watch (you can't share a suica between phone and watch, but you can attach more than one suica to the watch, so the watch was temporarily holding both suicas) - then forced an icloud backup from my old phone, unpaired the watch from the old phone and paired it to the new, and then was able to move one of the suicas to the new phone from the watch. A little roundabout and obviously only an option if you have a watch.

It seemed to me that it wasn't otherwise possible to move the suica from phone to phone simply using apple pay/icloud, but I could be wrong. Plus there may be something you can do using the actual suica app if you can handle the kanji.