If you have sent inventory to Amazon to hold in their warehouses, you are able to use Amazon to fulfill orders from other NON-Amazon marketplaces. This is called multi-channel fulfillment or MCF for short.
Listing Mirror does have the ability to automatically send your non-Amazon orders to Amazon for fulfillment with the Fulfill orders setting, found on the channel integrations page. However, if you are wanting more control for which orders are sent to Amazon, manually filling orders will be the way to go.
Go to the Orders page in Listing Mirror.
Under Fulfillment Actions, click the fill icon for Amazon.
And that's all you need to do! You should get a success/error message after clicking the icon that will let you know if the order was successfully sent to Amazon or not.