Although the case back with the display glass will technically fit, changing from one to the other is not as simple as just swapping the case back. As Ash noted, the non-display back model has the inner antimagnetic cover in it, so the movement spacer (called the enlargement ring) is quite short. The cover snaps on the enlargement ring, and the cover presses on the inside of the case back, and this holds the movement securely in the case.
If you just swap backs, and remove the inner cover, the movement will not be held in place by anything. The screws that hold the movement to the enlargement ring, do not hold the enlargement ring to the case, so the movement can flop around unless you happen to have a very tight fitting enlargement ring in the case.
To do this job properly, the enlargement ring has to be exchanged as well as the case back. The new enlargement ring is much taller, and an O-ring goes on top of it to provide a soft and compressible surface for the inside of the case back to tighten on, which holds the whole movement secure in the case.
Cheers, Al
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