You can use Stock Sync to update the product category for products in your store. 

At Shopify, a Product Category is called a Product Taxonomy; you can find a full list of all product taxonomies in the lookup table here. (English)

The feed file can have both the ID and the product as below and Stock Sync is able to update the product accordingly.

For other languages:

For all feed that was created before 7th November 2022, Please do recreate the feed and add this field again since Shopify changed the field name.