Sublet question law

We have approved a new tenant based on your scheduled move-out date of Monday, August 31 st.

Since the new tenant may not move in on September 1, you will also have a prorated amount of rent due for September, even though you are no longer living in the apartment.

Do you think the office can do that? Why should I be responsible for prorated amount if I’m not living there? It’s that legal? I don’t wanna make a conflict.