How to find out the spec of an unmarked li-ion battery
Here is some method I found in eevblog but the capacity were known. I don't know if it is applicable to my case.

You need a multimeter and a laboratory power supply with voltage and current regulation.
Measure each cell and check the voltage. It should be between 3.6 V and 4.2 V. Put to one side any cells with a voltage below about 3.0 V. These are probably weak or failed cells and should be recycled.
If you have six cells that were wired to give 10.8 V and 5.2 Ah, then the pack would have been a 3s2p arrangement and the capacity of an individual cell should be about 2.6 Ah.
Take one of the cells with a voltage above 3.6 V and try charging it with the power supply. Set the voltage limit to 4.2 V and initially set the current limit to 500 mA. Put the cell on charge and check that it accepts charge. The power supply should be in CC mode, the cell voltage should slowly rise and it should not get warm. If this is OK, you can increase the current limit to 1 A or even 1.5 A and continue charging.
Eventually the voltage should reach 4.2 V and the power supply should switch from CC mode to CV mode and the charging current should start tailing off. When the charging current decreases to 200 mA you can stop charging.
If you want to check the capacity of the cell you will need to conduct a controlled discharge and measure the current over time. A data logging meter is helpful for this. Otherwise you can just use a load like a 6 V 6 W lamp and record the current every 5 minutes or so by hand. Discharge the cell down to about 3.3 V under load and then figure out the capacity as average current times discharge time.