The solution that has been gaining good success in the US has been to externally expand the breast with external breast tissue expander 1st then inject the grafted fat. Need to prepare the ground for the new fat cells...
The diagram below explains that external expansion increases tissue space in the breast so that it will be able to house the new fat cells.
In summary, after external expansion with external breast tissue expander, the recipient breast is enlarged because of enlarged tissue space, this allows the injected fat cells to happily take up residence in the new location.