I have two Mark I*** SMLEs.
On one, the 1904 LSA, they simply replaced the whole rear-sight assembly with a Mark III type.
On the other, a 1907 Enfield Mark I* converted to I*** by the Navy, they left the original rear sight as much original as they could, just reground the ramp. The bed still is screwed directly onto the barrel, those lovely water-buffalo-horn buttons still are there and so is the original wind-adjustment assembly, merely with the V-notch reprofiled to make a U-notch.
When it comes to Mark I*** rifles, it seems that almost anything went, depending on who did the conversion.
Hope this helps.
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