SOLVED
The next day, Aeo on Mac asked me which different version I wished (iPhone or Mac): I chose the newest (that on the iPhone) and it was transferred to the Mac.
It evidetly needs its time… 
Hi, maybe a silly question (I’m a newbie), but…
I wrote a narrative timeline in the Mac version and it was in the iPhone version. Good.
Then, when my Mac was away for assistance, I’ve made some adds in the mobile version.
With my Mac back and it and the iPhone online, I’d expected to see adds in the Mac version too. But they there are not. The file is in the iCloud Drive folder.
Maybe the move is one-direction only (from Mac to iPhone)?
Or what am I wrong?
Thanks in advance for the help.