Sorry, I can't help you. "Lens" only has one 'e'.
Just kidding. But $300 dollars isn't much for lens in the 300mm to 500mm range. There's
this. That's not too fast, but it is very cheap. 1.4x teleconverters aren't too expensive, and it would get her to 420mm f/8, which would be pretty much useless in all but full sun. AF probably won't work at f/8 either. They also have
this. It's no faster, but is probably built better and might be a little better optically. Hit the used stores and check eBay, she might find a deal.
There's no 500mm lens worth having for $300 I'm affraid.
Hope she gets what she wants. She's very talented.