How to hang wall cabinet in fridge cavity wall?

[sunflowerz]

Hello!

I am in the process of making/ installing a cabinet above my fridge - today when removing the cornice I found this bracing ply behind the gyprock. There is a electrical cable which I can see as it runs to the socket. I have also found the studs with a finder but one is very close to where the cable runs. The cabinet will be kinda heavy as its 900mm wide plus the load of cups when full so I'd like to attach it properly. 

I was wondering what the best way to attach the cabinet would be?

Thanks.