This is a heads up for other people who might be looking for the same information in the future. As far as I have read, due to the Abflussprinzip, the costs should be claimed in the year moving costs have been paid by the employee, i.e. the year X. The tax amount paid for the steuerpflichtig (taxable) reimbursement in year X+1 should be swallowed. It is, in theory, free money/bonus for the employee anyway.
NOTE: Please do not take any action according to this message, it is only what I would have done if I would be the one filling this form in real life. When reading this message, please take into consideration that I have NO KNOWLEDGE on German tax system. My German is also mediocre, I am researching the tax use cases from my circle of friends, myself and Internet as a hobby, with the intention of studying the way of German collective thinking. The fun and improving my German comes as a bonus. Feel free to correct me in any way.