As a historian of religion, I do know a lot about Islam AND I have Muslim friends. I can assure you that no well-brought up Muslim girl or woman would invite a total stranger of the opposite sex into her home, if she lives alone. So either the young woman lives with her parents or is married, if she meant her invitation as your son thinks in a purely friendly fashion.
Obviously, some Muslim women are prostitutes, so that might be a possibility, or she could be even more devious and planning as someone suggested to cry "rape". Other scenarios present themselves to my cynical mind too, she could be a pickpocket, or have a husband or brother at home ready to do the mugging.
If your son is interested in getting to know this girl better then his only possibility is to invite her to a café for a cuppa in some other, preferably distant part of town, unless he invites you, his mother, along as chaperone.
However, he should realise that no religious Muslim girl can marry a man of another faith without running into very real difficulties with her family and the local imam, and living with a man she is not married to, is out of the question as well. So unless your son is contemplating converting to Islam, my advice would be to steer well clear of this girl and others like her. There is definitely a sub-text here, that is quite impossible to read when none of us was in the street when and where the incident occurred.