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Update to iOS 11.4. Open the Settings app. Tap your name. Tap iCloud. Tap the switch next to Messages.
If you haven't already done so, update the operating system on your iPhone to iOS 11.4 or later. Read "How To Update iOS" to learn how to update latest version of iOS on your iPhone or iPad. The Settings app has an icon that resembles two gears. It's on your home screen. Your name is at the top of the Settings menu next to your profile picture. This opens the Apple ID menu. It's next to the icon that resembles a blue cloud. The Messages or iMessage app has a green icon with a white speech bubble. This enable iMessage messages to be stored on iCloud.