CarstenE:
The only question is, there must be a little difference in the behavior, so that the software can divide between the uno and the adapter.
With your Uno on Serial2 you connect Rx to Rx but with your USB-TTL on Serial3 you connect Rx to Tx. If you replace the Uno with a USB-TTL adapter it must be connected Rx to Tx like on Serial3
Have you tried the USB-TTL adapter that you want to use on Serial2 in place of the adapter on Serial3?
If that does not solve the problem then you need to draw a simple diagram that clearlt labels all the connections in the working system and in the non-working system. Then post a photo of the diagram - see this Simple Image Guide
...R