Note: Make sure you’re signed in to the same Send and reply to messages on iPhone and Forward text messages from your iPhone to other devices.
To see Messages stored in iCloud, open the Messages app.
Note: If you want to turn off Messages in iCloud on your Mac, deselect Enable Messages in iCloud. You can choose to disable Messages in iCloud for all your devices, or just your Mac.
For more information on how to use Messages on your Mac, see the Update macOS on Mac.