The subject line is the answer, but here’s the longer story.
I recently switched iPhones. Through a series of stupid errors, I ended up having to set it up as a totally new phone instead of transferring my old phone data over.
Ever since I did that, some conversations refused to sync between Messages on my iPhone and Messages on my Mac, even though they were both set up properly and various online tutorials didn’t help me solve the problem.
That last tutorial hung me up on one particular detail though. The Text Message Forwarding option was not appearing for me in the Messages settings on my iPhone.
I figured this was just, once again, an outdated tutorial that hadn’t caught up to changes Apple had made in the Settings app. But… those screenshots looked current. Hmm.
I don’t even remember exactly how I made this mental leap, but I found the solution not in anything to do with Messages, but rather with the FaceTime settings.
Due to the long and complicated history of Apple’s online services, I have two separate Apple IDs. One I use for App Store purchases, and a different one I use for iCloud.
Well… on both the Mac and the iPhone I had Messages logged into my iCloud account. But on my iPhone, I had FaceTime logged into my App Store account. And that’s why the Settings app wasn’t showing me Text Message Forwarding in the Messages settings.
I logged out of my App Store account for FaceTime and logged into my iCloud account, and suddenly the Text Message Forwarding option appeared under Messages. I turned on forwarding to my Mac and my iPad, and now everything is working!