I am using the attached adapter. It should empower a circuitry with 4A for one hour (4Ah).

As a reference I have a 9V block battery, rechargeable, 200 mAh.
How are you figuring that?

Batteries in series, yes the volts are added. Amps are not. The amp output will be that of the weakest battery in the pack. If your batteries are 200mAh, then you can run a circuit drawing 200mA for one hour.