I do see a way around this one though CDR. It is his gun, he owns it. It is not one that is being transferred to him. So, providing there is no reason he may not legally own/possess a firearm, if upon his next visit home, he were to simply ensure it is not loaded nor is there ammo in any mag that might go with it, secure it in a locked gun safe such as a Gunvault Nano than lock the safe in the trunk of his vehicle, he could simply take it home himself. It is my understanding IL will require him to register the gun in his home state of IL, but under this scenario, he should be able to get the gun home. Obviously, should his parent simply ship it to him legally via UPS using a FFL in FL to ship it to a FFL in IL all the legal issues are avoided.
Technically, the gun was transferred to the father when the son left it in Florida with him, if the father had unrestricted access to it. There could be a claim of "storage" if the father did not have access to the gun, like it was in a locked safe that the father did not have the combination or key to. If the son comes back to Florida, he is still a resident of Illinois, visiting Florida. If he takes possession of the gun again, he is "OBTAINING" that firearm from an out of state source, his father who has complete unrestricted access to the gun in the complete absence of his son, and then returning to his home state with it. That violates 18 USC 922 (a)(3).