I have found on Prestashop 1.5.6 there is a new storage system. To enable the move of images to this new system you have to:
1.- Edit your config/settings.inc.php file and set shop creation date “in the past” earlier than 2013-03-26. Why? The stores more recent to this date will already use the new storage system, so no move is required. The situation is weird when you have installed an old version of Prestashop after that date.
2.- Then, edit controllers/admin/AdminImagesController.php
3.- Look for “// No need to display the old image system”
4.- Below the comment line I found: “$this->display_move = false;”
5.- Replace by: “$this->display_move = true;”
6.- Then go to Preferences -> Images and click Move Images.
7.- When it will be done – change code as before or leave it.