I'm assuming that the surgery is to remove her gallbladder?
I'm going to use that assumption for my answer.
In digestion the liver produces bile and sends that bile through a duct to be stored in the gallbladder (the gallbladder is located right beneath the liver). In the gallbladder bile becomes concentrated, making it more effective for digestion. Bile is used for the digestion of fats, which only occurs in the small intestine (there is also a duct going from the gallbladder and liver to the small intestine for this purpose. Proteins are digested in the stomach and small intestine, and carbohydrates are digested starting in the mouth with salivary enzymes, and continue to be diested into the small intestine as well.
Fat can only be digested in the small intestine using bile. When people have their gallbladder removed they lose the ability to store and concentrate bile. However, since they still have the liver producing bile (and after gallbladder removal some livers will produce extra bile in compensation for lost storage), fats can still be digested.
Basically, if your gallbladder is removed you can eat whatever you want, but your digestive system may be sensitive to excess fat intake if the liver cannot produce bile fast enough. This can cause diarrhea. So as long as your friend limits her fatty food intake she'll be fine.
My anatomy class lecture last year