I just got an email reply from my soldier that the package I sent 10 days ago safely arrived in Afghanistan - I got all teary eyed - which means I can start sending more packages and letters now.
In case there's anyone else from Poland who might need the info on how to do it successfully:
My package contained toilettries and was about 1.5 kg (3 pounds) and was sent via priority mail. I had to fill in the CP 72 form (standard for international packages). There's very little space on the form to list the contents of the package - only 3 items - so I also filled in additional CN 23 customs forms IN QUADRUPLICATE. Fill all forms in English, include the estimated weight (in kg, so put e.g. 0,25 for small items) and value (PLN XX) of each item.
If the post office clerk argues that the CN 23 form doesn't exist, they are wrong, and I suggest you speak with their superior. It is also a good idea to tell anyone who questions the validity of an APO AE address that "you asked at the main post office (or US consulate) and you're following their instructions". This little lie worked like a charm for me.
The CP 72 and CN 23 forms are, of course, not suited for APO addresses. The way I filled them:
Nazwisko: "your soldier's full name"
Firma: "Attn: Any Soldier"
Ulica: your soldier's address (anything that comes before APO AE)
Kod pocztowy: (left blank)
Miasto: APO AE + zipcode
Kraj: GERMANY
Two pros for putting in GERMANY as the country. 1 - You'll still pay a lot for shipping, but the rates are lower than shipping to the US. 2 - The package will get to your soldier faster because it won't be making a round trip across the ocean.
Remember to check the "podarunek/gift" checkbox on both CP 72 and CN 23. Additionally, on CP 72 in the "Wskazowki dla nadawcy w przypadku niedoreczenia" box in the bottom right of the form, check "doslac do adresata na podany adres" and write "ADDRESSEE'S COMMANDER" in the space below (this option should be free of charge).
That's it!