When Wave Warp is applied with Pinning set to Left Edge, the pixels along the left edge remain fixed while the wave effect affects the area to the right.
By using the Transform Effect to move the masked and animated portion along the x-axis so it aligns with the left edge, Wave Warp can hold (pin) the pixels of the left edge—such as the edge of a character’s cape—while the rest waves naturally.
Afterward, the cape can be moved back to its original position along the x-axis using Position, maintaining the Left Edge for Wave Warp while aligning the animated cape with the static part of the image. This makes the masked area blend seamlessly, as if it was never separated.
.
.