For what it's worth....
In their Supplemental Offence Report, Davenport and Bardin wrote that "at 3:30 Captain Fritz of the Homicide Bureau advised Officers to take the 38 S &W snubnose (Ser # 510210) that was used in the shooting and 3 live 38 shells and [we] also turned these over to Capt Doughty of the ID bureau"
https://texashistory.unt.edu/ark:/67531/metapth338163/m1/1/
Gerald Hill wrote a duties and actions report for Curry on 5 Dec 1963. In this account, Hill, Carroll, and McDonald turn the pistol over to Homicide detective TL Baker at "approximately 3:15 PM." See here: https://texashistory.unt.edu/ark:/67531/metapth337502/m1/3/?q=gerald%20hill
From this, it would appear that Hill gave the pistol to the Homicide squad ~3:15PM, and they in turn handed it to Davenport at ~3:30PM, tasking the latter to turn the gun over to the ID Bureau. Given this, there's no discrepancy.
Thanks Mitch,
This is how an argument should be presented with actual links to the primary evidence instead of the usual "trust me I'm a pretend defence attorney", it's like trusting someone to state the actual times but on closer inspection after my own research I quickly realized that one of the disputed times came from a months later recollection which quite specifically specified "approximately", so again thanks Mitch for doing the required research which seems to be a bit too much for members who at the merest face value want to cry foul for the slimmest of dishonest reasons.
This whole episode reminds me of Earlene Roberts who says that Oswald came in to the rooming house at around 1PM and stayed for
"not over 3 or 4 minutes-just long enough, I guess, to go in there and get a jacket and put it on and he went out zipping it.", which somehow equates to meaning that Oswald left at precisely 1:04PM. And some members even try to dispute the whole getting and zipping up the jacket because Roberts was blind in one eye, but in the real World she could see well enough to do her job and watch television, I just guess some members are truly pathetic!
JohnM