Hi! Thanks for your reply!
Yes, roaming is on. Yes, it's been restarted multiple times since he's been in Germany. Still nothing.
Oh, except ... it just started working -- for calls, anyway. I have no idea what could have changed. The only thing we've done is attempt to start a My Vodafone account for him this morning, which I gave up on when I discovered that in order to do so he would need to receive an SMS. But when I picked up the phone to double-check everything just now, I saw that (somehow!) the confirmation code SMS for My Vodafone had arrived.
Am still having trouble sending and receiving SMSes and iMessages, and the browser doesn't work (it says he's "not subscribed to a cellular data service".) Will try restarting the device again now...