Is it permissible to take some used furniture from an official residence after vacating it, and purchase a water cooler as a substitute to clear one's conscience?

If the employers permit you to take the furniture, or if they dispose of it, then there is no blame upon you for taking it, and you are not obligated to compensate them. However, if they do not permit it, then it is not permissible for you to take it, and your responsibility is not discharged by compensating them, because it is an exchange that is not valid without their knowledge and consent.