Again, tell your girlfriend to ask her doctor.
I am on depo and i'll tell you what the doctor told me. I'm just repeating my doctor's info, but I could be wrong so just please tell your grilfriend to ask her doctor.
You are supposed to recieve your first depo injection during your period. If you recieve the injection while you're on your period you're protected immediately. Like the second after the nurse sticks you in the butt with the needle you can go have unprotected sex and it's supposed to be okay.
However, if you get your first injection while you aren't on your period, it can take up to a month to become protected.