You can sync your text messages across Apple devices by enabling the iCloud messages sync feature. Synced messages will all be viewable in the Messages app, whether you're using an iPhone, iPad, iPod ...

Messages is designed to sync across all your devices logged into to the same iCloud account. iMessages sync by default; SMS/MMS and RCS messages sync if you’ve enabled access to them from your iPhone.

The sync between my iPhone and Mac messages had finally settled down, messages were in order, etc, and then I upgraded to iOS 12. Now certain threads will receive messages on the iPhone but not the ...