Hi Dougie, sorry for any previous confusion.
First, on further inspection I think looks like a turm II, with battle axe on the left side and possibly Olympic rings on the front, I assume (with no proof) that there is a mirror image? battle axe on the other side. The picture is rather small and low resolution but I believe approximately where the old 3.7cm would have been there is a man standing on the deck. This picture is annotated:
U-505 leaves Lorient under the command of Peter Zschech. The boat's former emblem -the battle ax- is visible on the port side of the conning tower. Zschech left it there as a token of continuity between the two commanders. But on further thought it must be a turm IV, unless she was originally rebuilt with a turm II which was upgraded to a turm IV before she sailed on her 5th mission
On pages 85 and 86 of Steel Boats there are pictures of the U505 after the bombing by Flt. Sgt Sillcock which show a turm I and shows the area of the deck where the 3.7cm gun was.
The quote from Steel boat page 145 is:
For the next two weeks, our boat underwent repairs. They also replaced our huge four-barreled 20mm anti-aircraft gun with a newly designed single barreled Oerlikon 37mm automatic cannon. The trim little weapon worked flawlessly for us until the very end.
This paragraph is after the description of the 5th patrol during which the boat suffered from several suspected sabotage failures and several close depth charge explosions.
I have seen the 3.7cm M42 and M43 incorrectly described as Oerlikon in other publications. I believe it is used to allow people from the allied countries to visualise the weapon and its performance.
There is at least one other reference of the veirling being fitted, but I am unable to find it at this time.
Also on page 137, after Flt. Sgt. Sillcocks bombing of the U505 and repair, including the turm IV upgrade:
Next came the ammunition loading. Our boat's new armament made this a simple task compared to the old days, because the boxes of 20mm ammo were much easier to handle than the massive 105mm artillery rounds we used to store. That big quad-barrelled flak gun inspired a lot of confidence that we will be able to fend off attacks by aircraft.
The fitting of the quad 2cm is also mentioned in Hunt and Kill, as you say, which I am currently reading at work, so don't have a copy handy
Regards
Jon