Thank you for telling us about your successful encounter, I was most impressed wiht several things, starting of course with the success, your son's GF ended up getting to the assistance she needed.
It sounds like a pretty desperate situation and I admire the way you have handled it. It is very easy to lose one's head and you have done the opposite, having sought out appropriate advice from Headspace and then used your local police who I'm glad to say, were in a position to help.
Getting via proxy the young lady to reveal her location must have been difficult, frustrating and very worrying - but you got there.
The other thing that I really liked was your son attracts enough confidence his GF looks to him in a crisis, partly no doubt due to your upbringing of your son, which has also led him to regard you as the person to look to for effective understanding and assistance.
Looking to the future I'm sure you son will need support, and possibly you may too, after all this is an ongoing situation, it probably does not just end just with this occasion. So may I suggest you and you son get together to work out what will make you both better able to cope?
I'd expect you would have already thought it may also be appropriate for the young lady's family to be involved, depending on circumstances.