Amazon FBA is supported by StoreAutomator.
If you received an order in which you do not have any quantity available in your default warehouse but quantity available in your Amazon FBA warehouse, you can fulfill the order directly to the customer by creating a fulfillment order on the order details page. To do that:
In Orders Menu, click Sales Orders and click the order you want to fulfill.
On the order details page click the Fulfill button on the top right corner.
Choose from the available warehouses the quantity to fulfill
Click send to create fulfillment orders to Amazon FBA warehouse.