Conversion to .22 is "possible".
Among the changes:
Fitting a new barrel, OR re-lining the existing barrel.
Altering the bolt to a rim fire design. (MAJOR job).
Converting the action to either a single shot or adapting it for a .22 magazine.
The military sights would not work as adjustable sights due to the totally different ballistics, so you'd either permanently reset the sights for .22, or replace them with a commercial sight.
However, the problems are finding a gunsmith who's qualified to do such a major re-design and re-work.
Second problem is, people who can do this level of work DO NOT work for minimum wage.
His first question is going to be "Say bud, just how much money DO you have"?
Bottom line: Finding a qualified gunsmith will be tough, and cost will be VERY high.
There were kits made by Numrich years ago that had a .22 rifled tube that fit SMLE"s,and came with a rim fire bolt.I found one 2 years back so they still turn up.Gun Parts Corp may still have the bolt parts.With a bit of lathe work a liner could be turned in to a slip in liner like Numrichs,but time is money if you cant do it yourself.