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I say yes, for a number of reasons.
The most basic is that I'm constantly exchanging matter with my environment -- I'd guess that there are very few atoms in my body that were there (and certainly not in the same place) a few years ago.
Does that mean I become someone new every few years? Of course not.
Another line of reasoning is that there is absolutely no difference between a basic particle here and a basic particle taken from somewhere else -- they have no memory. If I took a book and copied it, the letters in the copy would have different origin but would be the same letters -- the story would continue to exist in its original form.
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