As long as the battery is pandora it will work with the PSP Slim , so there could have been a few ways of creating a pandora battery
A PSP Phat which already has custom firmware running could have been used.
Now even A slim which has custom firmware can create Pandora battery using
hellcat's Pandora installeras confirmed by memeber shafiqdms1.
Its also possible to hard mod a slim or phat battery, not reccommended for the un-skilled, as Iv seen many reports of dead batteries.
And places like ebay, datel and diveneo sell read made batteries, in two versions one for slim and one for phat, with these pandora type batteries, they cant used for normal operation, only downgrading.
If you buy from ebay you should be ok, there are different versions of the magic memory stick but in essence, their all same, achieving the same goal, of which is getting custom firmware running on the PSP, installation may vary too, but nothing is drasticly different were one is more complicated then the other