I do have Text Message Forwarding on. It still won't forward certain messages. I am also having trouble syncing the devices. When I had the battery replaced, they named the Mac differently than what it had been named. When I finally figured that out, I changed the old name to the new. That's when the bulk of messages forwarded and were synced. But there are at least three different phone numbers/people whose messages will not sync. One is an iPhone, two are other brands--if that has anything to do with it. The Mac has the message histories on these, but only up to the date I had the battery replaced.
I also notice that even when I sync the devices by cable, not everything that was syncing before is now. And although it will sync photos, it gives me an error message that the Mac is not recognized.