What causes implant to move towards the armpits? How can this be prevented? 3 weeks post op.

Hello and thank you for your question.  Either the pocket isn't tight enough laterally to keep the implant from being displaced into the armpit, or some people request the "side boob" look and want the implant placed wider.  

Implant displacement is a well known undesirable outcome of some breast augmentations.  It can happen when implants are properly selected and not enough support is given to the breasts postoperatively.  Also, when choosing an implant size some patients actually request or do not mind when the implant is shifted towards the side of the chest ("side boob as they call it").  This means that the width of the implant is excessive.  This may be due to the desire to have a wide implant creating both cleavage and some implant show along the side.  When the implants are placed above the muscle, there is less tissue to prevent this happening. 
In my experience, a properly chosen implant along with a good post operative bra can prevent this if it is your desire not to have this happen.  I tend to like Caromed bras because they are very stabilizing and keep the implant going in directions you want them to go and prevent them going in directions you don't want them to go. A nice form fitting bra can be very useful in preventing unwanted displacement of the implant.
Surgically, over the years I have tended to make the pocket only as large as it needs to be for the implant to be inserted and remain in its position without folds. My desire is that the implant stays in the desired site without 
When you revise these complications, the pocket for the implant is much larger than the implant itself.  This allows the implant to shift considerably making the excessive pocket a fixed and permanent issue.  The surgical correction is to tighten up the sides of the pocket so that the implant remains more centrally located.
So, the main point here is that you have to maintain the position of the implant with a properly fitting bra (preferably prescribed by your Plastic Surgeon).  If it does displace, the surgical correction is not difficult.