There are actually several related questions, and it is unclear which one you are asking, so I’ll answer them all briefly.
1) How long does the landlord have to give notice of imposing a claim against deposit funds?
Florida Statute 83.49 says the following: “Upon the vacating of the premises for termination of the lease, if the landlord does not intend to impose a claim on the security deposit, the landlord shall have 15 days to return the security deposit together with interest if otherwise required, or the landlord shall have 30 days to give the tenant written notice by certified mail to the tenant’s last known mailing address of his or her intention to impose a claim on the deposit and the reason for imposing the claim.”
If the landlord fails to follow this statute, he/she forfeits any right to make a claim against the deposit.
2) How long does the tenant have to object to the landlord’s charges?
The same statute says “Unless the tenant objects to the imposition of the landlord’s claim or the amount thereof within 15 days after receipt of the landlord’s notice of intention to impose a claim, the landlord may then deduct the amount of his or her claim and shall remit the balance of the deposit to the tenant within 30 days after the date of the notice of intention to impose a claim for damages.”
3) How long after I move out can I bring a suit for my deposit.
The statute of limitations for written instruments is 5 years (FL Statute 95.11). So, if your lease was written, you have 5 years from the time you move out. If it was an oral lease, you have 4 years.