I think so, lugs and case look identical in both watches, so they should be interchangeable for both generations.
That may also be the reason why the (much cheaper) Gen3 straps have been withdrawn so quickly, otherwise many Gen4 users would buy Gen3 straps. In this way they are forced to buy the Gen4 straps, which are much more expensive… although Gen3 owners are also left without a good feature that their watch had: a very reasonable price for their straps
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