Once you've connected the Shopify integration to Heartland Retail, you must fulfill sales orders in Heartland Retail - not Shopify - for the integration to work properly.
If you fulfill a sales order in Shopify that will trigger the synced order to cancel/close in Heartland Retail and will not capture the sale or remove the inventory.
After the sales order has synced down to Heartland Retail, you'll need to distribute the items and fulfill the invoice. Check out this article to learn more about how order fulfillment works in Heartland Retail.
Heartland Retail will use Shopify's payment service upon order completion to charge the customer's credit card and complete the payment. Payments in Heartland Retail will be reflected as "Shopify payments".
If you've already fulfilled a few sales orders on Shopify, we recommend recreating the order in Heartland Retail then use a custom payment type as a place holder for the customer credit card (already charged in Shopify).
Check out this article to learn how to create custom payment types in Heartland Retail.