I have installed the 64-bit version of Opera 43 web browser and copied the (64-bit) Pepper Flash files to usr/lib64/opera/plugins but Opera doesn't see the plugin and Flash is not working...

Have you tried to install the original flash: https://get.adobe.com/flashplayer/

Yes I have the official Adobe Repo installed and the Flash player works with Firefox, Chrome and Vivaldi... but not with Opera. As Opera and Vivaldi use both the Pepper Flash Plugin I cannot figure out why it works with Vivaldi but not with Opera....

I bet you followed the instruction found on opera web site. Used to work a few weeks ago.
I did a reinstall yesterday and these instruction didn't work so instead I downloaded the RPM from adobe website and install it with yumex. (flash-player-ppapi-25.0.0.127-release.x86_64.rpm)
It created a file /usr/lib/adobe-flashplugin/libpepflashplayer.so
and flash is now enabled in opera.

From the about page:
Adobe Flash Player
Version: 25.0.0.127
Shockwave Flash 25.0 r0
Location:
/usr/lib/adobe-flashplugin/libpepflashplayer.so

Cheers.