To mel5141, The factory records show that it was scoped at the factory and sighted in with the scope, so not a stretch.
bushveld, the rifle went back and was re-chambered to flanged magnum and re-proofed.
I suspected that your friends lovely H&H DR was re-chambered as many of the original H&H .375 Flanged Nitro Express 2 1/2" rifles were after the H&H .375 Flanged Magnum was introduced about 1912.
I assume that your reference above to the records of H&H showing the DR being scoped at factory was the original 1907 configuration as a .375 2 1/2" Flg. NE.
After it was re-chambered and re-proofed to H&H .375 Flg.Mag, do the H&H records show that it was then re-regulated to group shots with the scope mounted upon the barrels? If not, and in my experience in building and regulating DR barrels of .375 range calibers if your friend mounts a scope on the barrels he needs to expect to have the barrels regulated (de-soldered, new Holland type front barrel brace made[if it has the H&H type] to spread or converge the barrels, re-soldered and re-blacked), Further even if the DR was re-regulated at Holland's after re-chambering/re-proofing with a scope mounted. and your friend now attaches another scope and rings the scope/rings are unlikely to have the weight and mass distribution of the previous scope/rings to where the barrels will now group.
If you are not familiar with regulating DR barrels here is a link for you: https://www.vintageguns.co.uk/magazine/the-barrel-regulator
The significant difference between the H&H double rifle regulation and the description of the process from this "vintageguns.co" link is that after the completion of the regulating at the range, the DR goes back to the workshop to have a new front barrel brace machined/made via a milling machine to the exact distance in thousands of an inch between the front barrels and the exact diameter of the front barrels made and then fitted/soldered to the barrels---this brace incorporates the front sight ramp.