Depends on Florida law. If Florida law requires that all handguns be registered and you want to keep the weapons in Florida, you may choose to get a receipt and register them as required. The other alternative would be to move them to the nearest state that does not have a registration requirement. I have always chosen door #2 because I believe gun registration is unconstitutional.
There is no requirement for registration of guns in Florida. Furthermore, there is no database through which the police could run the serial number. The only record of your father ever owning those guns is the Form 4473 he filled out when he bought them from the FFL. The FFLs are required to keep them on file for twenty years. The police would have to obtain a warrant to access those 4473s, for which they would need proof that some kind of crime was committed.
Even if your gun is stolen, and used to murder somebody, according to Florida law, you have no obligation to report it to law enforcement. There is also no requirement for you to involve the government in any way, shape or form when doing a private transfer.
You do not need a receipt for the gun, but like stated earlier it wouldn't be a bad idea. However contrary to what Daniel7723 stated.
There is a data base for all weapons. Although it doesn't show information like owners, it does list whether the weapon was used in a murder, hold up, etc. And, the police can and will access this system at any time. You can go to any police agency and request them to run the serial number to check and see if it is wanted, that way you will know that the gun is "clean".
Even though nothing can be done to you if you are found to be in possession of a weapon that was used in a crime and you were not involved in the crime in any way shape or form (you purchased the weapon after the fact). The police can and will take the weapon from you and you have no recourse in this, and obviously the police will have some questions for you.
But, again no you don't need anything for the transfer of ownership.
I know this because I am a cop in FL and use the system all the time.