There were four types of rear sights for the Number 4 rifle. The best is the "micrometer type" Mark 1 rear sight. The "L" flip type is the Mark II sight. The Mark III rear sight is a stamped version, but it requires a small spacer washer also. The mark IV rear sight is the Mark III rear sight with an improved catch and does not require the washer.
Your question is a bit ambiguous. If it is to inquire if a Number 4 rifle can use a NUMBER 1 MARK III type of sight, then practically NO. It could be done with a lot of dollars and a good machine shop, but not really practical.
For about $35-$40, you can buy a Number 4 Mark I (Type I) rear sight, and easily change it out for your present flip type Mark II sight.
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