The chief differences between No. 1 Mk. iii and Mk. iii* were
1. the rear sight windage knob was dispensed with (hence the right rear sight protector sticks funnily out to the right, allowing for you to look out for a windage enabled sight and replace the simpler one, if you wish),
2. (of interest to you) no magazine cut-off. This is however a device riding above the magazine and not integral with the magazine itself, so mag should be the same, especially given that post ww1 they reintroduced the magazine cut-off. The cut off was seen both as an economy feature, but more so as a safety feature, preventing inadvertent chambering of rounds.
Buy the magazine, should fit fine in theory. Note, sometimes Enfield magazines need tuning to work perfectly. Pay about NZ$50.
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