Don't have a photo, but the aircraft guns had a bushing in the end of the shroud like the .30 BMG ground guns.
<Edit> Found some photos...
The .50 BMG aircraft gun is very similar to the .30 BMG ground gun, just on a smaller scale.

The bushing in the end of the shroud is called a "booster." It helped to push the barrel backwards from gas pressure and acted as the front barrel bushing. You can see the cylindrical machined feature on the front of the barrel that rides inside the bushing. The M2HB ground gun had a heavy barrel that I doubt would have functioned well at high g-loadings cantilevered out from the receiver with the relatively short barrel support. The receiver itself was the same though. If you remove the barrel support and barrel from an M2HB you can install the barrel and shroud with the aircraft parts.

FYI, The M3 was a post-war .50 BMG variant used in aircraft like the F-86 that had a higher rate of fire due to some different internal components, a slightly different receiver and a larger diameter buffer on the back plate.
AG pilot wrote:
Stunningly beautiful!
Can anyone post a picture of the way the barrel jacket/shrouds go over the barrels in this installation (P-47). Are standard aircraft barrels used, and if so, is there a barrel bushing at both the muzzle and receiver end on the jacket/shroud?
Thanks.