Synopsis of the problem:
Albert Einstein, On the Electrodynamics of Moving Bodies, 1905: "From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B..."
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Einstein's conclusion: "the clock moved from A to B lags behind the other which has remained at B"
Einstein's conclusion is non sequitur - it does not follow from Einstein's 1905 postulates. The following two conclusions do follow from the postulates but involve no meaningful prediction:
Conclusion A: The clock moved from A to B lags behind the other which has remained at B, as judged from the stationary system.
Conclusion B: The clock which has remained at B lags behind the clock moved from A to B, as judged from the moving system.