Dear Panyuming,
Good question.

Kirchhoff current laws give the answer... currents into/out of a node must sum to zero.
So the 1st battery is almost charged and will be around 14 Volt as will the output of the charger.
The current into the node from the charger = the current out to the battery, so sum = 0.
Now close the switch. The 2nd battery is a low SoC so its internal volts will be << 14 Volt.
Therefore current will flow out of the node into the 2nd battery. and the voltage at the node will (potentially) drop depending on the output impedance of the charger.
Therefore current will flow from the charger to 2nd battery, and, if the voltage at the node has dropped below the open circuit voltage of the first battery, also from 1st to 2nd battery.
Here's a simplistic simulation that shows the 2nd battery V3 drawing ~5.2A, ~2.9A from the charger, and ~2.3A from the 1st battery (v2).
This will continue until the voltages of both batteries have balanced and then both will charge until SoC = 100%.

Wish to know:two batteries (each 120 Amp) currents:  120 Amp
Load current: depends on the used Inverter type 2.5 KW or 5KW
on the 2.5 KW type, You can draw up to 2.000 Watt.

Will do TESTING this weekend.