Message forwarding across multiple devices

I saw an sms message come through on the lock screen of my partners iPhone, it stated his iCloud address at the top.

What I'm trying to work out is if it was a message for him, or one he'd sent on another device but then shouldn't it say the senders name or is it possible he sent it and he had some sort of multiple device thing set up from either his mac or ipad that forwards on. When you send a message and you have forwarding on will it be displayed on other devices with your iCloud address. Just need to work out if this was a message he sent out or a message was sent to him.

It had a green icon so it looked like an mms message.

Sorry I'm not that great in explaining things