[us-virginia] Apartment Wants To Charge Me A Full Month Of Rent When I Move Out On The 10th, But Is Also Allowing Someone Else To Move In The Next Day, But Not Paying Rent Till July?

Hi!

I am a recent grad and moving out of my apartment. My apartment is trying to charge me my entire rent, when I move out on the tenth. Usually, I assume this is so they can inspect, clean and do any repairs. However, The girl moving into my room is a friend and signed a "no walk though" which means that the apartment complex is allowing her to start her rent the day my lease ends on the same day. The apartment is refusing to prorate my rent while also having someone essentially live on my dime. So I am wrong for thinking that this is wrong or might not be legal? I brought up prorating when signing my lease and my landlord told me "they would look into it" and then didn't change anything in the document. So I have kinda accepted that I am having to pay this month, but is it wrong that I feel like it is slightly illegal for them to just allow someone live in a residence I payed them for an entire month for?

Edit: They are making us both pay full rent for June. 1400 dollars for one month is crazy.