I see. Thank you for clarifying the situation for me, Michael.
You should typically provide her with 30 days written notice under these circumstances. Then, if she does not move out within that period of time, you could initiate a petition in the local court seeking an order of eviction
The biggest problem you may have is that it could potentially take longer to obtain such an order than the length of the lease. Because of that, you may wish to retain a local attorney to communicate with her, threatening litigation if she does not move out within the 30 day period in an attempt to persuade her to move out voluntarily and avoid a lawsuit for eviction.
She could potentially delay any suit beyond the term of the lease, especially if she continues to pay half the rent, but if you provide her with 30 days written notice today, that will start the clock ticking to get an order of eviction if one becomes necessary.
Here is a link which summarizes the eviction process under FL law:
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