I found that the Raspberry Pi serial interface rs232, described in a older post by myself, was too bulky.
Pi and AVR should be connected through a less amount of wires.
So I’ve searched the best hints to solder a cheap and uncomplicated level converter, that can directly be connected between the GPIO of the Pi and the rx/tx pins of the microcontroller.
On the German website http://www.elektronik-kompendium.de/sites/praxis/bausatz_pegelwandler-mit-transistoren.htm I found a useful circuit with transistors and resistors that I had in my toolbox. (something similar but also matching parts)
The following images are showing my circuit diagram and the test setup.
The first test worked flawlessly both in the direction to the Pi and in the direction to AVR microcontroller.
The third picture shows the circuit diagram used and the fourth image the development on breadboard. Now I can connect my test board and the Pi over normal jumper cable to have hanging around without various additional boards.