Is an employee entitled to keep a sum of money from the company's trust to compensate for material damage incurred due to sudden changes in his workplace and accommodation? If not, should he donate it on behalf of the employer?

This matter is subject to the contract. If the contract stipulates your right to compensation for damages due to the sudden transfer, then you may claim it. You may take it without informing her if she withholds it, unless that leads to harm to you. You are not allowed to take more than your right. However, if the contract does not stipulate this, then you are not allowed to take anything from her money or give it away as charity; rather, you must fulfill the trust. You can mitigate the damage by renting out the apartment to someone else for the remainder of the month.