Charging 18650 battery with built-in PCb
You should be able to charge it using the two wires with any Lithium Ion or Lithium Polymer battery charger. The circuit board seems to just be a protection circuit. You just need a charger with some sort of output connector (rather than the type designed for cells to be inserted in the charger). The capacity of the cell is probably 2 to 3.5 Ah. Charging at 1A or less should be OK.