I have a friend who was recently deployed and I wanted to send her a postcard. This was the first time I've ever sent mail to an FPO, and if you've never seen one they're not much more than a combination of letters and numbers, with no country listed.
I started wondering if I would even be able to send something from Japan. It seemed likely that the people in the post office would look at me like I was crazy and ask what country I was trying to mail it to, and then I wouldn't know enough words to try and explain. I did a quick google search and found some websites that claimed mail to APOs and FPOs can only be sent by the USPS, but then I found a page (in English and Japanese) on the Japan Post website assuring that they could send postcards, letter, and small packages to both.
With the website in Japanese ready on my phone and prepared to tell them "Beikoku Guntai" (American Military) if I was asked any questions, I went to the post office ready to make a fool of myself. But it was the simplest thing ever. The lady at the desk didn't even bat an eye and clearly knew what an FPO was. It cost the exact same amount as mailing a postcard to the US, and was perfectly easy. I know this isn't likely to be a common question for expats living in Japan, but I wanted to share my experience since I found conflicting information before I tried it myself.