No, i'm pretty sure that the three rings passed on from Middle Earth. That's why Galadriel, Elrond, and Gandalf all went, besides the fact that they could. Yes, the ring would probably be in Valinor!
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'But Melkor also was there, and he came to the house of Fëanor, and there he slew Finwë King of the Noldor before his doors, and spilled the first blood in the Blessed Realm; for Finwë alone had not fled from the horror of the Dark.'
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