8x57 IR (or JR) is the rimmed version and will not fit any M 88.

While the military made the change to the "S" bullet early in the 20th century, the majority of 8 mm hunting rifles remained to be offered with the "I" or 7.80/8.07 bore.
"S" barrels in hunting rifles were rather the exception than the rule.

The RWS Handbook from 1940 (!) describes in detail how this duality should be finally resolved.
One of the actions was introduction of the 8x57 IRS!
After WWII, the plan was retained (at least in Western Germany) and no new guns produced which used the old "I" or 7.80/8.07 bore.
fuhrmann