Does the faucet fit inside the cupboard and behind the washing machine?

Yes! A compact and flat wall faucet fits behind the washing machine. An example can be seen here. If you have a different type of wall faucet, there are three options: 

1. You can choose to turn the faucet a quarter of a turn, so that everything stays concealed in the cupboard.
2. You can place the faucet next to the cupboard, so that you can easily access it. 
3. You can install the cupboard 5cm from the wall, so that there is a 10 cm-wide space for pipes. See the technical drawings.