You might be looking for a vignette. There are many ways to make one. If you want exactly what was in image A on image B I would do the following:
Put both images in the same file, on different layers>> Use the magic wand tool (w) set to 0-10 tolerance click on the white edge in image A>> click on your layer for Image B and hit delete.
The vignette from A will not be applied to B