Hopefully you get the situation dealt with in an agreement that is fair and equitable to both of you. I'm sure that before you rent the room again that you will have some sort of contract for the next tenant so that you don't have to go through this situation again.
I'm sorry that you didn't receive the appropriate answer in time here. But it sounds to me like you owed him the money. Unfortunately, without a rental contract, you as the renter have very little power in the situation. More simply stated, he could leave any time, and he had a positive balance of 1 month + 9 days. You shouldn't have taken first and last with an agreement in the first place, really. Hope this helps someone else in a similar situation!
You should have had the contract made. There is no legal way to solve this since there is no contract. Otherwise you would get to keep your money.
This is precisely why you must always use a written agreement of terms before entering into any type of business dealing of this magnitude. This way, you have a legal recourse. The "last months rent" is also called the security deposit by some. This means that any repairs needed after thte tenant leaves will be taken out of the amount of the last months rent. The remaining amount (if any) is then returned to the tenant. There is usually a required term for notification of relocation. The tenant may be penalized by notifying before the specified time (if the contract states).
You guys should have made a contract, but since none was made, just try to find a mutual agreement that is a good middle grounds for the both of you. Best of luck!
Having no contract is a huge no no especially if the tenant is dishonest and does not want to pay rent. Another reason for having that contract is if lets say your tenant did not pay rent and he or she tries to sue you then you have the proof in court saying that they did not pay the rent and did not follow the contract agreement.