What can I do to move a file to a new folder and leave its import image as plane intact? I'm organizing my blender files and realized when I moved a file that has an image on a plane in it, it lost access to it and the plane just shows pink. I hadn't realized the image was never made part of the blender file, it just pulls it from the original image file whenever I open it. 

Now I know I'll take advantage of that in future by placing imported images in folders with their blender files so I can modify them if I want. But I'd like to change the path this file uses to find the image it is using. Otherwise I'll have to learn to use the UV/Image editor to re-apply it, which I think will take longer. I'm not into that kind of work yet.

Can I go into the file in an editor, find the path, and change it?
Alright, I found it now. I clicked on File > External Data > Find Missing files, and the File Browser opened, and I clicked the 'Find Missing Files' button on the top right. The folder open in the File Browser needs to have the image in it or it won't work. If you aren't sure where it is, you can click the top entry in the System tab at left and have it search the whole hard disk, or click the up arrow at the top of the folder and file list in the main window area until you are confident it must be somewhere in there.

The image was tinted deep magenta after I did this, but it was there. Closing the file and reopening it caused that to disappear, it was an artifact.