Ahhh - stupid me! (In Köln/ Germany we would say: "Ich Koppelschoap!"
)
In the backend of the original website I found the "solution".
An old Joomla version (1.5) is installed there and for the translations there is JoomFish included - not JDiction. In the configuration I can also only see the database type Mysql. After I had contacted the hoster say said Mysqli is not offered in this webpack. So that is why JDiction isn't running correctly.
Sorry for this confusion! On all the websites we are working on we have included this extension of yours. And it always works well! So I did not expect to find such an "old" website installation and so I surched for the fault at the wrong place
We are going to move to another hoster now and after this I'm sure everything is going to work good like it always does.
However thanks for your support and all the best to you!
AW