Does Fat Move To Other Parts of the Body After a BBL?

Fat cells  that don't survive after fat transfer to the buttocks, are simply aborbed by your body. Fat cells that don't survive release their liquid fat contents which are absorbed slowly by the body through the lymphatics (small vessels that absorb edema, protein and fat outside the blood stream). From the lymphatic channels they eventually are brought  to veins and eventually the byproducts are used as an energy source (just as a candy bar is). Sometimes if too much liquefies if forms an "oil cyst" that can be removed by syringe aspiration

Hello dear!!
Thanks for the question and provided information as well. 
After a BBL, only about 70% of the transferred fat cells will survive, so it is normal to see only a minor reduction in your buttocks. If you have any concerns, I suggest you to follow up close with your plastic surgeon.
Good luck :)

The short answer is: Not if there is little or no weight gain after surgery.

My personal favorite candidates for BBL (liposuction and autologous fat transfer by injection)  are women who want shapelier bottoms and who also have relatively poor waist definition and unwanted excess fat elsewhere on their bodies.These patients can look forward to a true "win-win" outcome: a shapelier figure with a smaller waist and rounder, firmer, fuller buttocks. Not everyone gets the full increase in buttock size that they dream of because 20% or more of the injected fat is commonly lost in the process. However, reduction of the back, waist, abdomen and thighs is more certain and a smaller waist can give a more "hour-glass figure" and make the buttocks look better and larger even if the grafting is slightly disappointing. Thus the "win-win".

I caution all liposuction patients to be mindful of their weight after surgery. Losing a few pounds is a great idea; it will tend to smooth out any small irregularities. On the other hand, weight gain of more than a few pounds can theoretically magnify minor subcutaneous imperfections and turn a good outcome into a lumpy one.

When liposuction of an area such as the waist and abdomen is aggressive and thorough, the number of fat cell in these areas is significantly reduced. This means that excess calories taken in after surgery aren't likely to be stored at those sites and must be stored elsewhere. New fat will have to accumulate in new areas that probably were not liposuctioned. This is good news if those excess calories go to the transplanted fat in the buttocks and many patients will be happy if these calories go to increase their breast size. The bad news is that weight gain after liposuction may go to unwanted areas such as the face, arms, thighs and inner abdomen. I say  "bad news" because these areas can be difficult or impossible to correct with liposuction. I've seen both the good and the bad and always urge patients to be careful.

There should be no change in body shape and no "movement" of fat after the initial surgical transfer has settled down if a patient's weight is stable.