The FFL will execute a Form 4473 and put the firearm on the business register. When you come to retrieve it, another Form 4473 is executed to transfer the firearm from the FFL to you. My wife just did this for a suppressor purchased 3 years ago. It remained in the safe at the FFL until the ATF tax stamp arrived. A Form 4473 was executed to transfer her property and take it off the FFL inventory.
I have no idea whether a law enforcement agency has a clear property management process that removes you as the "owner/possessor".
You're giving bad advice re this subject. First, you posted in "news" and it's been moved to "chat." Now you admit you "have no idea."
This is a reckless thread.