The short answer is no. The person would have to be an exact tissue match which would be either a clone or identical twin. Otherwise the fat would be rejected or immune suppression drugs would have to be used. Here's a news item to help you understand the "cost" of transplant surgery. The first face transplant recipient just died from complications of the immune suppression drugs she was taking.
Is it possible to use donor fat from another individual for brazilian buttocks if they receive lipo at the same time?
Doctor Answers 3
BBL and fat donor
You can not have fat transferred from another individual. The fat would not take unless they were an identical twin. Organ transfer is done with patients on immunosuppression drugs which have significant side effects. This is not performed for fat transfer.
No, fat can not be used from another person for your procedure. Fat is living cells and it is similar to a transplant. You can only potentially get fat from an identical twin.