You can either duplicate the category itself (and choose in the proposed options to make the products visibles in the new category) or create the new category first and ask PrestaCategories to move the products (to change their default category).
In fact their are mulitple ways to achieved this with PrestaCategories, in a minute. Just depend on the result you look for.
One common point to all methods: The products are never duplicated, but they can be made visible in differents categories. This way, a modification made to a product applies to all categories it belongs too.