The change from MkIII to MkIII* only officially involved the magazine cut off. Although they were removed, some just before and other at the time, the volley sights and windage adjustable rear sights are noted in the LoC as able to be present on both models.
In Australiaicon the SMLE reverted back to the MkIII and the magazine cut off for all production from the early 1920’s until mid 1941.
Although not likely, it would not be wrong to have a windage adjustable rear sight.