Moving fat from one part of the body to another seems like a dream, and with some limited exceptions that is what it is, only a dream. It is not difficult to liposuction fat and inject it in another location. What is difficult is to make the fat survive.
When fat is moved, its blood supply is interrupted and much of it may not survive the transfer. Without blood the natural tendency is to convert the fat to calcium which requires less nourishment. The result is that small nodules of stone-like material form in the layer below the skin.
One way to reduce this problem is to transfer small amounts of fat. For this reason fat transfers work quite well in the face. It is used for the nasolabial folds (between nose and mouth) and the deep creases in the middle of the forehead (glabellar creases) or frown lines. It may have a place to fill in some defects created by over zealous liposuction. Another quite successful use is to fill out contour irregularities in scars. In some cases an alternative treatment is the use of filler injections, like collagen.
In general, fat injections should not be used in the breast. The small calcium deposits may look like cancer, and mammogram results are less reliable. If you are considering breast augmentation, think of other methods instead of fat injection.