Yellow Triangles With Explanation Points in Windows Movie Maker

I'm using Movie Maker to make a documentary. I save my work on a flash drive.  I add all of the pictures on to it and it works fine as long as I only use it on the computer I edited it on. However, when I save it and move the flash drive to a new computer, it displays the dreaded yellow triangles with explanation points in the middle instead of the images. It has the option of "Finding the images" where I have to search through the flash drive for the pictures, so I do, but then it will only work on THAT computer and not the original. I really don't feel like having to search for the pictures every single time I need to edit or present. How do I fix this issue?