iOS 11.4 and the upcoming macOS 10.13.5 High Sierra have a feature called Messages In iCloud, it syncs all your Messages between all your devices. I really like this feature. However, in iOS you actually have to activate it. Here is how you do that.
Messages In iCloud
Go into your Settings area and tap on you iCloud Identity at the top of the window:
You will see this window. Now tap on “iCloud”:
You will be taken to this screen:
When you first get to this screen, the Messages slider will be off. To activate Messages In iCloud just slide it to the “On” position.
There is a caveat here though. When you activate Messages In iCloud all your messages on your iOS device are transferred to iCloud. This frees up space on your iOS device which is great. However, if you only have limited space in iCloud it may cause a problem. If you only have the Default 5 GB space in iCloud you might try this, but just keep an eye on how much space it uses.
I really like the Messages In iCloud feature. To me it is really helpful to monitor my messages on all on all devices wherever I am.