I committed a crime in Georgia. In 2007 an in 2011 Georgia filed charges on me. I pled guilty in 2012 and was put on 5 years probation. I have never lived in the state of Georgia and have lived in forida for the last 5 years. All of my vehichls are registered in fl I have a home there and own a business there , my children and my wife also live and go to school there. Georgia has sent a probation transfer request to fl. Do they have to accept it?

All of this should have been arranged during court and in plea agreements.

No Fl does not have to accept it, if there are good reasons not to.
As a matter of practice, yes they almost always accept it, if you show place to live and job there. Where your cars are registered means nothing.

It can take from one month to amost three months to get transfer done.