You have damages in excess of his security deposit? You have the last month's rental which is due or it extra money? If you hold extra money and have extra damages you can hold that money against your damages. Make sure to properly impose your lien against the security deposit. Follow the statute.
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Unfortunately, landlord/tenant law is an area that is governed by both statutory and contractual law, as well as decisions handed down by appellate courts. Thus, they are very fact specific to your particular matter.
First, you must look to the contract and the obligations/remedies that the contract provides for both parties. It may speak to what you are allowed to do with over payments. It may also speak to whether you have waived your right to seek attorney's fees under Florida Statutes if you are successful in suing on a provision of the lease. Second, I am slightly confused by your question. Was the tenant month to month and terminate the tenancy by moving out or did the tenant leave one month early from the end of the tenancy.
Again, landlord/tenant matters are very fact specific. I would suggest that you retain a landlord/tenant attorney to advise you on your situation.
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If he left early and did not give proper notice, you may also be able to charge him additional rent. However this isn't clear in your facts. You should review this matter with an attorney. Many attorneys offer a free consultations, including my office, where we can fully evaluate the complaint, your situation and goals.
My answer is going to assume that you are not using the early termination / liquidated damages clause that you are allowed from Florida Statutes 83.595.
Once the tenant left the premises, you could have chosen from three choices, according to 83.595 (the fourth one is by itself and must be chosen at the beginning of the lease, it is called early termination or liquidated damages):
1. take the premises back and consider the lease terminated. You can't charge any rent once you retake the premises in this scenario and you must not charge for it on the tenant ledger.
2. take the premises back and try to rent them, considering the lease continuing unless and until you can rent them. You can charge a rent charge on the tenant ledger up until the day the next tenant moves in.
3. do nothing (probably the only use for this is where a trust fund continues to pay the rent even though the trust fund baby has abandoned the premises).
So, unless the written lease agreement say otherwise, you should only charge for rent up until the day your son moved in if I am reading your facts correctly.
You should be using a tenant ledger, where you write down charges and total the far right column to find the balance.
If there is a balance after adjusting the ledger to not charge for December's rent or part of December's rent, then you write the security deposit claim letter and ask for the former tenant to pay the balance.
If there is a credit, then you write a check and send it with the letter.