Why the actual charge current of a battery is not improving when I shifted to larger current capacity battery charger power supply?
You can't. 

It will draw the current it needs to charge at the correct rate.  

Lithium batteries respond poorly to improper charging - "explode, catch on fire, burn down your house" poorly. 

The thing you are calling a charger is actually just a power supply.  The actual charging circuit is part of the battery pack, and it is designed to keep you battery pack from going "boom."  That means that (among other things,) it regulates the charge current going into the battery.

The charging circuit will use as much current from the power supply as it was designed to draw.  No more.  A power supply that provides the proper voltage will not "push" more current through the charger than it is designed for.



Just because the power supply can supply more current, the charger doesn't have to (and won't) draw more current.

A power supply that can supply more current does not mean that your battery must charge faster.