thank you for finding an issue with the paths to examples. Nevertheless, we are going to move all examples to GitHub. There is the example Dominik wanted to show you:
The more popular examples are also here:
This example uses a loop made by wire on the CORE2 board between hExt UART TX pin to hSens3 UART RX pin. You can additionally connect the RX pin of HC-05 module to this loop and you should see the same message on USB Serial and Bluetooth serial port console.
Your code looks well but have you done the initializing of hExt.serial before?