Many Amazon sellers do not know that Amazon will fulfill your eBay (or website or any other sales venue) orders for you. And the best part is that Amazon passes on their low UPS rates to you when they do that.
The way it works is simple. When an item sells on eBay (or any other site), find the item in your FBA inventory and click the box next to the item. Now look at the drop down box above your inventory listing and select “Create Fulfillment Order.” Hit the Go button and Amazon will bring you to a page that has a field for the address and the email address. Fill in the information and hit Continue and it takes you to a page that shows the shipping charge. It also gives you the option to select expedited shipping if that is how you sold it. Select the shipping and hit continue and Amazon will now fulfill your order.
Having explained all that there is a better way. I use a company called JoeLister that can help you create eBay listing from your Amazon FBA listings and fulfill the products automatically for you. I have been using them for several months now and its working out quite well. They not only automatically fulfill the order, they post the tracking to eBay and if your FBA inventory falls to zero Joelister will also zero out your eBay listing so you don’t sell something you don’t have.