P Phillips : thanks for trying to help.
Not irrelevant because I did not mark it as solved. I have no idea how to do that. It wasn't solved until late this afternoon.
I believe it was leroydouglas who marked the problem as solved after sending the response : "Verify your Messages>Preferences> enable SMS".
But I had already done that, among other things, and it had not worked.
Anyway, I investigated the problem further today and found that the recipient had actually changed carrier and the phone number was in the process of being transferred. In the meantime the phone had been allocated a temporary number. The transfer of the number is now complete and everything is working properly.
So now it is solved.