Terminal output disappearing after SSH into cygwin

[Martyn B]

Marco Atzeri via Cygwin wrote on 21.01.21 16:13:
> 
> very simple:
> 
> ssh <your connection> |& tee /tmp/ssh.log
> 
> 
> you can also use screen logging capability
> https://stackpointer.io/unix/linux-ssh-session-logging/564/

Thanks for the suggestions. I am aware of tee and screen and might as 
well even copy/paste the screen content before I terminate the connection.

Still I'd prefer to
1) understand why this happens. - Is this the Cygwin standard behavior?
2) thus hopefully learn a solution that keeps my server logins uniform 
and leaves the chronology of the terminal window lines untouched

I've posted the exact output and some additional information here:
https://sourceware.org/pipermail/cygwin/2021-January/247546.html