Shopify check out on Webflow store

Hi - I have a client that I built a Webflow ecommerce store for and now after a few months they want to be able to able to integrate with their in-store POS so they can better track inventory. Apparently going through Shopify is the only way to do that and so they are requesting to add a Shopify cart/check out to the Webflow ecommerce site. Does anyone know if this is possible? Or does the entire shop need to be moved over to Shopify?

Here is my site Read-Only: LINK
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