Research on the Sony Web Page on the battery counterfeiting resulted mutatis mutandis:
"How can I tell the difference between fake and original?
Sony batteries carry the Sony logo and a hologram for security against counterfeiting. The Hologram can be found on the battery or on the packaging either "
The supplied battery, the hologram is missing (the original battery and on the Amazon product photo available). On the packaging of the supplied batteries is also not a hologram to find. Instead of a colorless embossing the Sony logo (like the original battery and on the product picture) can be found on top of a gray Aufduck.
According to the description of the Sony Web Page that is a fake.
The significantly lower battery capacity is a clear indication that it can not be a Sony original part. The supplied battery showed already after a few uses a markedly reduced capacity than the original battery. The charging time to 100% is markedly shorter than the original, the battery was exhausted after a full load already after a short use.
I've got me a Sony original battery from your dealer. This product meets the authenticity criteria described by Sony and also has a similar to the original capacity.