Stall. Stall. Stall.
He may or may not be allowed to put you out immediately. There will be many factors to consider.
By "unofficial," I am assuming that you have not signed a lease. That is not a big concern, as leases do not always have to be written. What is important is whether "he" is the owner or the tenant, and what the lease (not your sublease) says regarding the ability to sublease the unit.
A well-written letter from an attorney to "him" would make him back off his threat to immediately put you out and probably buy you the two weeks you need to pay the past due rent.
You should immediately contact a FL lawyer familiar with landlord/tenant law.
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You are considered a hold over or tenant at will. The landlord will have to go through a standard eviction process to evict you. They will seek attorney fees and costs against the tenant for the expense of the eviction. The lease will not come into effect because you are not a signatory on the lease. They probably will sue you (sub-tenant) and the tenant that sub-let to you. They probably will not use "self-help" to evict you because that could expose them to liability if they damage your belongings. I would either try to reach an agreement with the landlord whereby you sign a lease or plan to move if you are not able to come up with the rent in the near future. The landlord may nor want to rent to you and you cannot force them to rent to you. If you submit the rent to the landlord and they accept it then you have entered into an agreement to allow you to stay the property for that period of timer hat covers the rent, the next month. If you pat two weeks late and they accept then you can stay for two more weeks.
I agree with the other answer- whether "he" is the landlord or the tenant may have some importance. Regardless of who is trying to evict you, you have been paying to stay there, so you are a tenant and they must go through the eviction process. If you wish a further free consultation on this, please feel free to call me at 850-778-1355.
My response to this question does not mean I agree to represent you in any proceedings. This information is also not subject to attorney-client privilege.