Nope. There's no master database that says "the AC adapter with this serial number goes with the laptop with this serial number." It's your word against theirs.
You'll have to buy a replacement AC adapter from your netbook manufacturer, or a universal adapter (make sure the output voltage is the same, the adapter's amperage is equal to or exceeds the amps of the original, and that the plug is the same size as the socket. Be wary of buying the cheapest replacement you can find on Amazon. They're often uncertified and ship straight from China. They often produce excess RF noise (technically making them illegal to use in the U.S. or EU), put out dirty power or the wrong voltage which can damage your equipment, and often are poorly assembled and fall apart after a year or two.
For future reference, pretty much everyone has a smartphone nowadays. Any time you return something or drop off something for repair, take a picture of it (with the return packaging or something identifying the repair shop in the background). If you're lending something to someone, take the picture with them holding the item you're lending. That way if in a few months they say you never lent it to them, you can just show them the picture to "remind" them.