Talk nicely to your neighbor about her cat, and seeing it standing out in the rain. She may not realize the cat may be suffering. Hopefullly she will providing some outside shelter for her cat, maybe a dog house to get out the rain.

If she doesn't provide shelter or care for her cat more, let us know and we will consider other options. Keep us informed how it goes. Its great the cat has atleast one person, ie. you, looking out for it.