PLEASE HELP CLARIFY THIS ISSUE WITH DEPOSITS...

Here's the situation:

Tenant came in 2/2017 with an annual lease, paying first, last and 1 month security.  He was never sent another lease until 6/2018, which asked for all new deposits and increased the rent payment.  Tenant sent letter saying that, as Landlord was already in possession of said deposits, only an extension agreement was needed, so did not return the signed lease, but did pay new amount immediately.  Landlord never sent the extension paperwork, but rent payments continued timely.

Fast forward: tenant, who is now therefore month to month, gives notice at beginning of July, and does not pay July rent since Landlord has "last month" deposit from when he originally moved into complex under an annual lease specifically noting "last and security" deposits.    

Landlord states that 1.) 30 days notice was required, 2.) now both deposits are security since there isn't a current contract in place, and that 3.) tenant must pay an additional month's rent.  He says he will return the two month's security after the tenant pays for July, and moves out.  Landlord has filed a 3 day notice and tenant is panicked.  (Fyi, in FL, only 2 weeks notice is required for month to month tenants.)

Aren't those deposits governed by the initial lease contract, i.e. if they were "last & security", rather than two months security, they remains so, even though the tenant became month to month?

Thanks in advance for any comments!