Restore/synchronize Messages history
On your iPhone:


Open settings
At the top tap your name/Apple ID
Tap iCloud
Make sure the switch next to messages is on


On your Mac:


Open Messages on from your Dock or Applications folder.
Click Messages in the Menu bar.
Click Preferences.
Click Accounts.
Click the checkbox next to Enable Messages in iCloud.
Click Sync Now to begin syncing your messages.


Your messages should now begin syncing.