Mojave - iPhone does not appear in iTunes

Hi - got a funny situation. I run a MacPro (mid 2010 / 5,1 - with Metal GPU), a MacBoolPro (mid 2012) and a MacBook Air (early 2015) and use also two iPhones (iPhone 5S and iPhone 8).

Both iPhones are on iOS 12 (latest available download).

The MAC's are all upgraded to Mojave - and they all work without an issue - EXCEPT one issue.
My MacPro is my "main" PC - and the iPhone's would not appear in iTunes!
Have tried both iPhones on the two other MAC's (with copied iTunes lib) and they work - not problem at all.

Interestingly - on the MacPro the iPhones are working with Photos as well as Apple Configurator 2 - not an issue.

So - what can cause this exception with iTunes?

Any idea how to resolve this issue - it is too strange to be true ;-) - at least from my naive User perspective.

Many Thanks.

Robert