Unless it is letter mail USPS treats mail sent to APO as international mail. You need a customs form on the shipment stating what is inside the package, country of origin and value. Pretty sure they won't clear any mail that violates country law. It no doubt would be prohibited.
Also there is this on Tobacco and APO
USPS modifies tobacco-shipping regulations
The USPS is changing its regulations of tobacco shipments from the US to military postal destinations. Shipping options to these areas will include Priority Mail service with delivery confirmation. Beginning 27 August, customers mailing to Army Post Office, Fleet Post Office, and Diplomatic Post Office destinations where tobacco shipments are permissible, will have Express Mail Military Service and Priority Mail service with Delivery Confirmation as shipping options.
The addition of Priority Mail service with Delivery Confirmation for the shipment of tobacco to APO/FPO/DPO destinations enables shipments of small amounts of cigarettes and smokeless tobacco products to service members in war zones and other destinations where Express Mail Military Service is unavailable. The Prevent All Cigarette Trafficking Act went into effect on 29 June, and subjects the mailing of cigarettes and smokeless tobacco products to new mailing regulations. The announcement modifies only tobacco shipments to APO/FPO/DPO destinations.
All other restrictions of the PACT Act remain unchanged. Packages containing tobacco items addressed to APO/FPO/DPO destinations are restricted to a total weight of 10 ounces or less. Mailers must show proof of legal age to purchase tobacco at the time of mailing and confirm that the addressee is at least 18 years of age.
