Is trading in Native american coral pieces legal? - Identifying

There are of course a lot of Native pieces which have coral in them, but I wondered if it is legal to sell coral? Or is this coral a type that is legal? I hope someone can explain this to me? Thanks in advance for your help!

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This vintage necklace is composed of beautiful red branch coral beads that are Italian. The coral is all natural and hasn't been treated or dyed in

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