Overlapping leasing legal?

[Joshua Cetnar]

I am currently renting as part of a temporary job. My work was to go from approx May 15 - Dec 15 so I signed a 7 month lease for an apartment. I was pro-rated for the first month so I paid for half of the month of May, but I was told the lease had to go through Dec 31. I knew that I was leaving before then and was upfront with the property manager that I would be leaving before the lease was fully up. I recently talked to him and confirmed my move out date with him, and he mentioned that he had someone who might move in a few days after I moved out. Their move in date would be before my lease would be up (let's say Dec 18).  Is any of this legal? I would love some advice as to how I should handle the situation. I don't have a problem with someone else moving in before the 31st, but I would like to be reimbursed for that part of my rent.