You would have had to use a knockdown drywall (kd dw) frame as you are going into a stud wall with the drywall already up. This comes in 3 separate pieces. There are "compression anchors" in the top of each jamb and pre drilled holes on each side of each jamb at the bottom.
If you don't have these holes at the bottom you may have to drill them as some frames don't have them but come with clips instead. If your frame is moving you either don't have these clips, didn't install the screws in these holes, and/or you didn't tighten the compression anchors at the top.
To install it you slide the head in place over the wall, install the hinge jamb by aligning the tabs in the top of the jamb with the slots in the head and pushing it over the wall, and install the strike jamb the same as the hinge jamb. Pull the head down tightly with the jambs and level by shimming at the base of the jambs if needed. Tighten the compression anchors, make sure the frame is square and level, and install sheet metal screws in the bottom holes.
Hope this helps and please let us know how it goes.