hello ExPLoR3R
Wellcome to the community.
Looking at your pictures, you should have 3 outlets in 3 different rooms.
Somehow you seem to have a regular phone that doesn’t run through the Connect Box 3. The outlet labeled “Amt” leads to this conclusion.
The cable runs from Amt to LAN 3 and not T+T. T+T usually stands for telephone+telefax.
The T+T outlets in the rooms should be the ones on top of the LAN ports. 
In order to establish a LAN connection, you’ll need to figure out wich LAN port in the cabinet is connected to the outlet in the living room and the office. Use a LAN cable to connect those ports and you should be able to hook up the computer to the outlet in the office and the Connect Box to the one in the living room.
Maybe you have to use the T+T port for the phone and get an adapter to connect the phone to make the LAN port available.
