Tenant Broke Lease 5 Months Early, Demands Last Month Rent Refund

[Daly O'Brien]

Recently purchased a property on Nov 9th. 

On Nov 10th a tenant moved out unexpectedly even though her lease was through March 2019. 

The owner before me had collected first and last month's rent, AND a performance bond that would be refunded after proper performance of the lease. 

I know that I get to keep the performance bond because she broke her lease, but am I required to give her the last month's rent back? At a prorated total (Nov 10th through Nov 30).

My thinking is that I get to keep her last month's rent money because she technically owes me the rest of her lease, 5 months of rent. Would appreciate some legal advice! Thank you!