Well, I don't plan to visit the cooling system again for at least another 100k miles but I'll try to use words to describe how to use the strainer wrench to hold the pulley while wrenching on it.
Simply hook the notched end of the tool on a nut on the pulley and the swing arm gets hooked on the opposite nut. That is it...you can now hold the pulley in place and knock the nut loose with a wrench.
This plumber's tool is made for removing large diameter locking rings (i.e. large plastic "nuts") on sink drains and what not. Some of those are quite large in diameter and the swing arm makes the tool universal for many different sizes.
2001 530i/5 (E39), Topaz Blue/Stone Green/Black (97k miles)
2005 545i/SMG (E60), ED Order, Titanium Grey/Grey (lease transferred...no longer have)