Here's the problem. Possession is basically 9/10 of the law when it comes to firearms. Your brother is in possession of the firearm, so even though you call it yours, in reality it is your brother's firearm. When you left it with him in CT, it was effectively transferred to him. This wouldn't be a big deal if you hadn't left the state, but you did.
Therefore, were you to go back to CT and take possession of the firearm, you would both violate federal law (he'd violate the law by transferring a firearm to a person he knows to not be a resident of his state, and you'd violate the law prohibiting you from importing a firearm into your state of residence that was acquired outside the law, outside of your state of residence).
If he were to mail it to you, you'd both violate the same laws. If he were to bring it to you in FL, you'd both violate the same laws.
The only legal way to do it is to involve an FFL in a way that meets both CT and FL law. The easiest way would be to have him ship it to an FFL in FL, where you can fill out the 4473 and take possession of the firearm.