How to determine maximum capacity of a battery in mAh? - received fake battery Is it an increasable value ? I think its not.

I just bought an extended 3890 mAh battery for my Galaxy S4 GT I9500. The original Samsung battery is 2600 mAh.

This is my second purchase from a different seller, after discovering that the 1st was a fraud. 
In Android tools, the new battery capacities say 2600 mAh only as maximum capacity.

I complained to the seller, and he suggests to do full charge cycles, re-calibration. However, that did not increase the capacity.

The seller is trying to prove that calibration can increase the capacity of the battery he has sold me to 3890 mAh as advertised. However, this doesn't look like it's gonna happen.

Most trusted tools for Android, CPUZ, 3CToolbox also say that the capacity is 2600 mAh only.
Battery calibration is a myth and definitely will not help you in any way. For details see my answer Bought a new battery. Do I need to calibrate it
3C Toolbox (and maybe other apps, not sure though ) read the battery information from the ROM files and not from the battery you have. This I learnt when I sought a clarification from the developer, when the app was showing battery capacity as 4000 mAh whereas the battery is 3100 mAh (Huawei Honor 6). To quote from 3C Toolbox developer mail


In Android, one can get the stock hard-coded battery capacity from battery profiles, an hidden API in Android. That’s the one of the 2 sources the app uses.
The other source is in the kernel, usually under /sys/devices/power_supply/battery/charge_full_design (On my device path is different). To know the path on your device, from 3C Toolbox, tap request support from Help and support menu. An email will be generated to the developer having information about your device, including battery_info.txt. This file amongst other things specifies the path of second source

When you change your battery and replace with an extended battery, the ROM information is not updated. To adjust the capacity of the battery manually (from Battery Manager → Tap the 4 small square icon → Adjust Capacity or use Configuration Wizard). This change is for this app usage only
How to measure actual capacity using 3C Toolbox  Your concern is on verifying the actual capacity ( which was mine too). This can be done by using the current sensor of your device. If your device doesn't have a current sensor, it derives from voltage sensor and may be less accurate (Edit (in 2020) , in recent Android versions most devices are required to have a current sensor, so you needn't bother checking if your device has a current sensor or not - they have it as a rule).
Here is the relevant portion of reply from the developer that should help you.

So in the end the only fully reliable way to verify capacity would be to pin the battery to an external meter. Less reliable is to use the current sensor when available and using my app you can get the actual capacity derived from actual measures of the sensor. For that the best is to use a 1 minute monitoring while charging, as sensors are often updated every minute using an average value (for the past minute). Sensors often provide very accurate results.

See snapshot below highlighted portion shows charge in 28 minutes.
(Battery Manager →Markers →  Choose plug state chargers→ Tap on the notification and set up monitoring settings)
Discharge your battery to say 10% and charge fully-you will know your battery capacity using this method


Hardware Measurement: If you want to rig up a testing circuit, this would help you How to measure capacity of a Lithium-ion battery or Li-Ion Battery capacity tester (Lithium power tester

Edit:  Neither does OEM description of the phone or apps like CPU-Z,  Hardware Info tell you whether your device has a current sensor  . You will need to spend time in searching if it has a current sensor. It is better to avoid that search, since we are looking at approximate capacity to determine if it is a fake. Hence, in 3C Toolbox settings, you could
set
Battery Manager →Markers →  Choose plug state chargers→ Tap on the notification and set up : Record all the time (on); mA retrieval method (automatic, if your device is not listed), Recording Interval -every minute while charging (accurate mAh calculation)

Edit:  For more details , please see Where are the battery capacity files located