Your friend really ought to ask his/her doctor about any "significant" pain s/he's experiencing (if s/he hasn't already); but in general, how long it takes for there to be no pain can depend on the type of fracture, where it was, how much strain the person puts on the fracture sooner than may be good, and any number of other things.
I've had "all kinds of" fractures (the only limb that hasn't been associated with a fracture somewhere is my left arm). My thinking is that a month "is nothing". I've fractured my ankle a couple of times, neither of which was a major fracture. Both times it took a long time before there wasn't shooting pain when walking. Even after the bone is healed there can be different types of pain associated with the injury. "Weird" muscle pain, pain from over-exertion or putting too much weight on the injury, pain from cold temperatures, etc. are things that (at least for me) kept showing up for ages (years), until, finally, all pain eventually disappeared.
A dislocated fracture I had in my right hand over 30 years ago is still kind of sensitive all these years later. It never quite went back to "good as new". With the fractures I've had that did seem to go back to "good as new", any pain that came after the initial injury was generally of a different nature than the pain that happened at the time of injury. It could be severe, but it was clearly of a different nature.
Some time within the last year I heard some sports reporter say that Patriots' Tom Brady had been "nursing a hairline fracture" for over a year. I don't know the exact story, but if a young, athletic, guy like that has been dealing with a hairline fracture for over a year that kind of says something about even minor fractures.
In any case, here's a "schedule" for how long things are supposed to take to heal: http://www.doctorsecrets.com/your-bones/time-to-he...