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The tag def appears okay, DS on bottom is correct. Some of the photos of the print are kinda blown out and not great. Without that info, if it was fake, they've installed a legit tag, and most modern fakes aren't a DS bottom. But if you take a higher quality photo of just the front print, can compare better.
Jimmy J
(Please note: Legit checks I do in this forum should not be considered 100% conclusive; I'm simply giving a gut reaction based on the limited information provided.)