N.
The Salvation Army came and picked up a garage full of stuff from me when I moved my mom from Dallas before.
She could also do freecycle where she lists everything and says that they must take everything if she wants to get rid of it fast. Of those two options freecycle will probably get the quickest response.
Have her go to http://www.freecycle.org/, select the areas she wants to list in, and all the directions will come to her thru email.