How can I get food shipped from Amazon to my APO/FPO address?

I've found out that Amazon has some APO/FPO shipping restrictions:

Originally Posted by Amazon

APO, FPO, and DPO Addresses

Most items can be shipped to APO, FPO, and DPO addresses, except:
cell phones and service
computers
furniture
grocery items
outdoor living items
Target@Amazon.com items

Additionally, some apparel, baby, camera and photo, electronics, health and personal care, housewares, jewelry, software, sports, and tools and hardware items cannot be shipped to APO, FPO, or DPO addresses. An error message will appear at checkout if you enter an APO, FPO, or DPO address and the item isn't eligible to be shipped to that address. Check the item's product detail page for eligibility.

How can I get grocery items (food) shipped from Amazon to my APO/FPO address?

Use freight forwarders (parcel forwarders, package forwarding companies) that allow to ship your purchases from any US online store to an APO/FPO address.