Stop Online Ammunition Sales Act of 2015

Amends the federal criminal code to require the licensing of ammunition dealers.

Prohibits any person except a licensed importer, manufacturer, or dealer from: (1) selling ammunition, with an exception for a sale of ammunition to a licensed importer, manufacturer, or dealer; or (2) engaging in the business of importing or manufacturing ammunition, or in the course of such business, from shipping, transporting, or receiving ammunition. Prohibits a licensed importer, manufacturer, or dealer from: (1) transferring ammunition to a person unless the licensee, in the physical presence of the person, has verified the person's identity by examining a valid identification document containing a photograph of such person; or (2) selling or delivering any ammunition (currently, any armor-piercing ammunition) to any person unless the licensee notes in his records the person's name, age, and place of residence, if the person is an individual, or the person's identity and principal and local places of business, if the person is a business entity.

Applies prohibitions applicable to the shipping or transport of firearms, and record-keeping requirements applicable to the importation, production, shipment, receipt, sale, or other disposition of firearms, to ammunition.

Requires each licensee to: (1) prepare a report of multiple sales or other dispositions whenever the licensee sells or otherwise disposes of more than 1,000 rounds of ammunition to an unlicensed person at one time or during any five consecutive business days; and (2) forward such report to the specified office and to the department of state police, the state law enforcement agency, or the local law enforcement agency of the jurisdiction in which the sale took place by the close of business on the day the multiple sale occurs.