I have a show folder for each year. I move the image file folder to there also. All the links are broken at that point.
Open your sequence, click on any picture file in the sequence, do a Ctrl A to select all effects, that should highlight all effects, then in the effect settings window, right click on the path to the pictures, and select bulk edit path, then select the location of your image folder. Render all, all should be good.
I know it is a pain, but it works. Maybe one day it could be fixed to recognize all paths in the show folder.