Although others have given some good advice, the reality is she is behind the curve in defending herself and is vulnerable to this guy.
Not necessarily her fault but a classic example of why people need to get some type of training in defensive tactics, [armed, unarmed, unconventional, etc.], before they need it.
Martial skills are not learned overnight and take a serious attitude toward defense of ones person and many hours of proper training to become adequate at defending your person.
Forget the sprays, they are not reliable enough for anyone to count on when the chips are down and do not always affect someone enough to incapacitate them.
A dog would be a good idea, but getting one now would really not help as the dog and owner need to "bond" and become comfortable with each other which takes some time. The dog will be in a new environment and not familiar with her routines and wants. The dog may give her early warning if it is a "barker" and she would be able to call the authorities at that time. The dog may also be a deterrent if it was big enough and the guy was the type who was afraid of dogs [ not very reliable to count on though ].
She should contact the local PD and have them file a restraining order against him. Our local "209a" restraining orders are issued if she feels physically threatened or he has verbalized threats to her. If she is contemplating taking gun training she must be in fear enough to meet that standard for a restraining order.
Though women are killed daily in the US while they have restraining orders issued against others it will put the PD on notice and give her some relief if he gets within the prescribed distance as set by the courts. He can be arrested if in violation and though not the solution, it neds to be part of the overall package in this situation.
I'd have a "big brother" stop by and have a talk with this guy. Then he knows he is dealing with someone other than the fairer sex. It could escalate/enrage him further or get him to understand she isn't alone in this matter and that others are aware of his unwanted presence in her life.
I may have to fly to Chicago in the next month to have a "talk" with someone who can't seem to grasp the concept of "let it go" and probably needs to be "wispered" to.
Hoping everything works out for your friend.
Brownie