One of my favorite features of Apple's iOS/MacOS ecosystem is the ability to share text messages across all devices whether they are Apple's iMessages or the conventional SMS text messages. There were a few bumps along the road while Apple was getting this working, but for the past year or so, it has been working flawlessly for me.
I started getting Not Delivered error messages when I sent an SMS from my iMac. But the odd thing was that they were actually being received by the recipient's phone. They just weren't being shared within my Mac and iOS systems.
I tried the usual things, rebooting, etc. Then this morning I posted the problem on Apple's discussion forums.
Immediately after doing that I realized there was one thing I hadn't tried: disabling text forwarding and then restarting it. Sure enough, that fixed the problem.
Here's what I did. On my iPhone I went into Settings > Messages > Text Message Forwarding and disabled forwarding on all my devices.
Then I powered the iPhone off and back on.
Next I went back into Settings > Messages > Text Message Forwarding and re-enabled forwarding on the devices where I wanted it to appear.