You can set up your Shift4Shop shop to accept orders going to US military shipping addresses. To do this, you must specify the appropriate APO "States" in your US Shipping Country specifications.
Setting APO "States"
Go to Settings > Shipping.
Under "More Options," click on the Country List link to view your store's selected countries.
Look for the United States and click on Action > Check States to the right of the listing.
Use the +Add New button at the top of the page to add your specific APO address (See below).
The APO Addresses are:
Armed Forces Europe
Armed Forces Pacific
Armed Forces Americas
4. Click Save to add each.
This will add these three APO options to the States drop-down on the Checkout process, allowing customers from these military locations to place orders on your site. Remember that you also need to have Shipping and Payment options enabled for customers from these addresses.