There are two possible ways:

1. If you want to re-arrange many products, the best way is to import them with new parameters. 

2. The other way is as follows:

  • go to the Catalog → Categories page
  • find the necessary category in the left panel, click it, then open the "Category products" tab.
  • press the "Remove all" button; the products will be removed from this category, however the products themselves will not be removed.
  • then go to the "Category products" tab of the destination category, press "Add products" and add all necessary products at once there.
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