Jani,
I am given to understand that before announcing the change from 8x57I to 8x57 IS (military only) the Prussians had all their stock of M88 Commission rifles (and the early M98 Mausers chambered for 8x57I) inspected and the ones that had large enough neck diameter to safely fire the new ammunition were marked with an "S" and had the sight components changed to match the trajectory of the new ammo. The ones that did not have large enough neck diameter had that area reamed to the larger diameter, the sight components modified and marked with an "S". This was kept a secret at the time to prevent potential foes from taking military advantage during the "changeover". Consequently, civilian 8x57I and 8x57 IR rifles were not inspected/modified by the Prussian Government and neither were the rifles that had been provided to the Prussians allies. It is not known if or how many of these other rifles were subsequently modified by the allies or private gunsmiths. After the "Great War" and the Versailles Treaty, it has been reported that Mauser reamed the chambers of their 8mm barrels with necks large enough for the "S" bullets while the groove diameter was for the "I" bullets. With the knowledge of these previous procedures, some gunsmiths reamed the necks of "I" chambers to the "S" dimensions and/or "freshed out" the barrel to the larger diameter.
An alternate possible reason for the out of line "S" on Raimey's rifle could be that it was originally made as an 8x57JRS but had to be marked with two different stamps because a single stamp for 8x57JRS had not been acquired when they restarted operations after being closed down.
As an aside, the "I" diameter was always the normal diameter for hunting rifles until after WW2 and it has been shown that those rifles with a large enough chamber neck (shown by testing a case fired in that chamber to see if a .323" bullet will freely enter) can be used with the larger bullet because it is when the case neck is "jammed" into a chamber too small to release the bullet that causes excess pressure rather than the smaller barrel diameter, as found by the Prussians before WW1.
Mike