Export order from woocommerce and/or shopify to another WooCommerce

This might be a bit tricky. I'm looking for a way to push orders from one shop to another.

I can't find anything by searcing.

What I'm trying to accomplish:

To create a plugin or similar that will add a "push to supplier" button to orders in the backend. The button should send the order data to the recipient store (the supplier) with all data (also the store information if possible).

I've tried looking for some kind of Dropship feature, and there are endless possibilities to use this when you sell products, but I'm looking to become the supplier website and that is tricking me.

Any ideas is welcome :)