On your iPhone or iPad, go to Settings
Tap your name
Tap iCloud
Turn on Messages if it is not already enabled
Open the Messages app and wait for syncing to finish
Connect the device to Wi-Fi and power
On a Mac, open the Messages app
Sign in with the same Apple ID
Go to Messages > Settings or Preferences
Click iMessage
Enable Messages in iCloud
Wait for messages to download and sync
To save messages locally on Mac, keep the Messages app open until syncing completes
To access messages on another Apple device, sign in with the same Apple ID and enable Messages in iCloud
To export messages from Mac, use the Messages app and copy or print the conversation
To back up messages from iPhone, create an iCloud backup or a computer backup