Weight and Balance in Airfreighters

If an airlifter takes off with 10 tons of pigeons in cages, it is obivous for everyone that the weight of 10tons need to be taken into the weight and balance sheet of the airplane.

But now we are in flight, and the ten ton pigeons are released out of their cages inside the cargohold and start all flying around.

Question: do we still have to take the 10 ton pigeons as load, and thus in our weight and balance sheets, or do we have to reduce the airplane weight by 10 tons?

Please give the scientific explanation also to the question and correct answer.