There are two ways to move the shoulders!
One from below, using the hands, or elbows, or even the upper arms. Most people putt using some or all of those muscles, voluntarily or otherwise. I think that a lot of problems people have with their stroke mechanics evolve from conflicts between various muscle groups..ie People trying to putt SBST with a tilted shoulder motion and a reverse rotation of their forearms or upper arms.
The other way is to move the shoulders with the muscles in the back and gut(mainly the obliques). So the mind is in the shoulders being MOVED. After a while, one doesn't think of them - it becomes your habit hopefully. Initially it is difficult, especially for handsy people, and especially with shorter putts, after all, how many things do we use our hands for? Gradually, you learn to love that feeling of setting up, aiming, and then allowing instincts to take over.