There is no export/import functionality within the Power Tools admin, unfortunately.

The process of setting up the filters in the Power Tools admin requires you to start from scratch, as there are one-time setup options so you cannot simply copy the filters from one store to the other, as these processes will not be run.

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Please note: you can copy your theme if you are using the same theme on both stores, which will save you from doing the installation step again.

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Also if your filters are tag based, you can copy the entire Filter Menu admin page and paste it into Excel, which will give you the list of tags in a column.

We also provide installation services. If you would like us to assist in the installation of the Filter Menu on your new store, please don't hesitate to reach out, an expert from Shopify Power Tools will be happy to help.