Stone is basically a unit of Mass. The unit Stone belongs to the system of units used in UK i.e Imperial System of weights and measures. On the other hand, kilogram or kg is also a unit of mass. However, it does not belong to the imperial system. In fact it belongs to the International System of units.
The conversion between stone and kilograms is very simple. I.e
1 stone equals 6.35 kilogram
1 stone equals 14 pounds.
Thus, 9 stones 9 pounds equals 135 pounds
135 pounds equals 61.23 kilogram which is the required conversion.