If it fits in the case physically, I would take a template of the PSU screw holes and apply them to the area where the PSU sits and drill them out on the case as opposed to drilling the PSU(voids warranty on the new PSU) Be careful not to allow metal shavings onto the motherboard if you leave it in the case.
If it doesn't fit in the case then you are looking to mount it outside the case which can be problematic as it looks like the fan on the original may be intricate to the CPU cooling, with that black shroud.