Opennet
From the pictures posted you appear to have a genuine No4(T) Sniper Rifle without its No 32 telescopic sight. You do have the Original No 8 case for the sight.
Your rifle appears to still have the original pds fitted to the side of the receiver, for mounting the scope bracket, as well as the original cheek rest fitted to the rifle butt.
Being a 1941 rifle it would have been originaly fitted with a No32 Mk1 sight which was upgraded in service to a No32 Mk3. The serial Number of the Mk1 sight has been stammped and then crossed out on the wrist of your rifles butt. The 24343 serial number of the Mk3 sight has then been recorded.
This may have occured by when the Factory Thorough Repar was carried out as evidenced by the FTR stamed on the wrist near the serial number.
It is good that you have the original scope case recording both your rifles serial number and the serial number of the Mk3 Scope.
To complete your rifle you need to source a Mk3 sight with a mounting bracket and then have them carefully matched to your rifle by a very compent Enfield experienced Gunsmith who knows what they are doing, such as Brian at BDLLtd. http://www.bdlltd.com
Brian sells a great little book that willl give you all the history of the No4(T) rifles "An Armourers Perspective .303 No4(T) Sniper Rifle and the Holland and Holland Connection" I highly recommendt that you buy a copy.
Whilst these sights are rare and very collectible, there is a suitable No 32 Mk3 scope, Serial 22499, with an reproduction bracket currently listed on Ebay. You need to be quick and expect to pay plenty Buy it now price is USD$2450. T32 MK III British Lee Enfield No 4 MK1 Sniper Scope Sniper Rifle Stock Pads | eBay