It must be very rare as there appears to be no mention anywhere of a Mk2* SMLE.
Maybe its a No2 ............................
SHORT RIFLE No. 2
Approved 28th April 1916 (LoC 17755) for Land Service, this is the first rifle made from up from an original SMLE Mk III, the .303 barrel was bored out and a .22 calibre liner inserted. Conversions were done by A.G. Parker & Co. Ltd. and Wesley Richards & Co. Some 1,743 conversions reported.