Move to iOS stuck at 1 minute remaining

I'm trying to use the "Move to iOS" application to move from Android to iPhone.

However, whatever I do it gets stuck at 1 minute remaining. I've tried many times and I've tried waiting for more than 24h.

I've read all what I possibly can on the subject. I've restarted both phones multiple times. I've made sure both of them are updated to the latest OS, etc. Both phones are plugged in and 100% battery. Phones a few inches apart. There's no SIM in the iPhone and on the Android phone I've disabled mobile data.

I've tried only transferring "Contacts" (which should be a simple task) and it will still get stuck a 1 minute remaining. So I doubt the problem is related to network issues. Indeed, if I forcefully cancel the process, I can see my data transferred and it does actually look like all of them. But I don't dare guessing. My gut feeling is that the application is re-calculating something after the network transfer is complete and it this "calculation" (or whatever it is) which gets into some kind of loop.

What really bugs me is that I have no way to narrow in on the problem. The Move to iOS application seems to follow Apple's general design principle: clean user interface is more important than anything (i.e. don't let the user know what is going on, it would not look good visually?). At the point where it gets stuck, what is it doing? No way to tell. Arghh.

Please help.