Chances are, she won't be able to find British style green beans (runner beans) in the States. Any sort of green beans are usually used in bean salad with the ones generally available in the States being typical.
Broad beans might be used in a salad, but not as a green bean.
ETA: looking at the recipe, if I couldn't find runner beans, I'd use two other varieties of fresh green beans and the fresh podded broad beans. If I couldn't find the fresh broad, I'd use canned rinsed fava and skip the cooking step for the canned beans.
I think this is where the British dialect has created an error in how people think about things. Like how Brits sometimes think of fractures as minor breaks or cracks when medically all broken bones from minor to the very worst are fractures. Saying "use runner and green beans" is a bit like saying "use cheddar and cheese".