From the Florida Lottery website:

Q. How can I claim my Lottery prize from out of state?

A. To claim prizes up to $599 by mail, simply fill out the information on the back of your ticket legibly, and mail your ticket, along with any correspondence, to the following address:

Winner Validation
Florida Lottery
250 Marriott Drive
Tallahassee, FL 32399-9939

Winner Validation will process your ticket and mail you a check for any applicable prizes. Because federal law prohibits the mailing of Lottery tickets across state lines, winners redeeming free Scratch-Off tickets, or free Fantasy 5 tickets, will receive a check for the retail value of their free-ticket prize. We cannot send additional tickets in lieu of a prize check.