Note that syntaxes like Microdata and RDFa don’t annotate the HTML, they use the HTML just as a carrier. After parsing the Microdata/RDFa, it doesn’t matter anymore which markup was used.
If your two properties with the same content belong to the same item, it’s not useful to have the additional one, as it doesn’t add anything new (but it’s not forbidden either):
<div itemscope itemtype="http://schema.org/Person">
<span itemprop="telephone">1234</span>
<!-- … -->
<span itemprop="telephone">1234</span>
</div>
If your additional property belongs to a different item, it’s not duplicated: a different item, a different thing:
<div itemscope itemtype="http://schema.org/Person">
<span itemprop="telephone">1234</span>
</div>
<div itemscope itemtype="http://schema.org/Organization">
<span itemprop="telephone">1234</span>
</div>
However, you should make sure not to add multiple items in a document that are about the same thing.
So if you’d have a Person item in the header, and a Person item in the footer, the problem is not that both have the same telephone property, but that you have two separate items in the first place.