@ more AA6YQ comments below
I did it, i.e. I used Realtek Audio in WinWarbler and the message was properly reproduced in the PC audio system.
Then I changed back in Winwarbler config>soundcard the "Phone Transmission" to the "microHAM CODEC" soundcard and..... the message(s) are correctly reproduced again via the radio.
Then it appears that now everything is re-shaped and that only the changing of the soundcard and the coming back to the correct one has solved the problem. I do not know why it happened, but I'm glad of the result!
@ It's unusual for a diagnostic step to solve the problem. Something obviously changed; it would be best to understand what, and how -- otherwise, the incorrect behavior could return -- and at the worst possible time.
@ Joe W4TV, any suggestions for how to proceed from here?
+ AA6YQ comments below
It is perfectly reproduced through VLC player and through the audio of the PC
+ Good. What soundcard is the VLC player configured to use? Temporarily configure WinWarbler to use the same soundcard for phone transmission. What happens when you active a phone macro in WinWarbler?