Fractures heal at different rates depending on the location in the body, any other medical issues such as diabetes, and at times the age of the patient. However, typically, a fracture can be considered healed around 12 weeks if it heals in a normal manner without issues, so it is reasonable to consider the fracture not healed at 6 weeks for your mother.
Many people will start to feel better at 6 weeks because the bones are getting "sticky" from a callus that is formed during the healing process, but this needs to calcify before it can become new bone.
I hope that is helpful,
Shaun Felcher, MD