Open Real Planning's tableau and go inside reservation details by clicking on the first day (image 1).
Image 1 - Click to zoom
Click on option Reservation split, choose the day your client will be moved and the room in which he will continue his stay.
Then click on the green button on the right to confirm the operation (image 2).
Image 2 - Click to zoom
The system will split the reservation accordingly (image 3).
Image 3 - Click to zoom