OK, OP, you said in your original post
The total rate is the same but it is a disadvantage for me as i can get the bf cost reimbursed...
So it is clear to me that you got an itemized bill.
The thing is simple. Let us say you booked a room for €100, and during booking you added breakfast for €13. So your total room rate is €113.
But to hotels, the underlying rate is different. You now have a Room rate with Breakfast for €113. However, for the hotels, it is €85 revenue for the room and €28 revenue for the F&B department. It is a revenue division for hotel's accounting department. It is really an internal measure of how your room rate will be divided to different hotel revenue departments.
You might have requested the reception on check-out and asked them to issue a bill for room and breakfast, that was the problem. Inexperienced agent might have chosen wrong format for the bill, unknowing what you were exactly looking for.
So what you need to do is to contact the hotel's accounting department if they have one, and request a bill that is
not itemized. The hotel should have issued a bill for the total payment and have your bill as Accomodation only. It is doable from hotel management interface to issue bills under different settings. The hotel should never issue a bill that shows internal revenue division any way, unless required by law.
So go back to the hotel and contact their accounting or front office manager, ask them to re-issue an invoice to show what you paid as Room Rate or Accommodation, rather than Room and Breakfast divide. If they said no, keep pressing the issue and tell them that you need it for reimbursement. I know from the hotel management system it is do-able. But if they insist they can not do then tough luck and do not go back to this hotel again.