Shopify & Pixels - Shipping Override Solution Needed

I am based in Singapore run an art store on Shopify.

Alongside my other art I now plan to offer framed prints from Fine Art America / Pixels.

There is an app that lets me import items listed on FAA / Pixels to Shopify.

The import works fine.

BUT a problem arises in the shipping costs.

I expected that since the items imported on to my Shopify store came from Pixels, the shipping from Pixels' fulfillment centre to the buyer would be calculated directly overriding the settings of standard shipping rates from Singapore that I have set on Shopify.

This does not happen. At checkout, it ignores the fact that fulfillment is being done by FAA and calculates shipping as per the flat rates that I have set.

Anyone have any idea what needs to be done to set this right?

Thank you in advance