I'm sorry, I'm not too fammiliar with the terminology, so I will clarify a bit more (so that I can understand exactly what is happening). With the osciloscope I'm measuring the difference between the A and B wires. The RS485Pi gives 0V (difference between the wires) for the logical "0" on the bus and the difference of 2,2V for the logical "1". So, you are saying that this is ok with the standard, since there is more than 200mV difference between the logical "0" and the logical "1". Do I understand you correctly?
But, to put it short, I solved the problem. I came across a document named "Specification and implementation Guide for MODBUS over serial line (http://www.modbus.org/docs/Modbus_over_serial_line_V1_02.pdf). And there I learned, that in some cases, you need "Line polarisation". This must be implemented if at least one device requires it. Unfortunately, the EVCO device has practically non existent documentation (at least not avalable on-line) and I didn't know I had to use it. Anyway, the polarisation means, you have to pull the line A to +5V, and the line B to the common line (ground) through 450-650 Ohm resistors. When I did this it started working immediately.
And I now noticed another thing in this document (page 22). It states that the voltage V0 is the voltage of the line A and V1 is the voltage for the line B. For the binary 1, V1>V2 and for the binary 0, V0>V1. So, in my case, the difference between V0 and V1 was 0, so technically this is prohibited I guess. I hope my interpretation is correct.
Anyway, it is working now and thank you for your help.