By Florida State Statute 196.071, 
"Homestead exemptions; claims by members of armed forces. -- Every person who is entitled to homestead exemption in this state and who is serving in any branch of the Armed Forces of the United States, shall file a claim for such exemption as required by law, either in person, or, if by reason of such service he or she is unable to file such claim in person he or she may file such claim through his or her next of kin or through any other person he or she may duly authorize in writing to file such claim."

Homestead Renewal
If you have homestead exemption in Duval County and receive orders to transfer you must  provide the Property Appraiser's Homestead Exemption Office with a copy of your Military Orders and a valid mailing address.  This  information is required for renewal of your homestead exemption. It is only needed if you are transferred away and intend to maintain your Duval County home as your permanent Florida residence.

Also, Florida law allows you, as a member of the Armed Forces, to rent your residence in your absence without loss of your homestead exemption.