Get to the other side of the barricade and open a large door. You'll notice Elizabeth and you'll begin your pursuit after her. Don't move too fast, because you should check each corner for valuable loot. The girl will be making it harder for you to catch up, opening tears with various obstacles. She will finally unintentionally become captured by Fink's men.
Enter a small room located on the left of the corridor. You'll find a Voxophone #35 here, as well as money and a grenade launcher hidden behind the desk.
Once you're ready to help the girl leave the building via a door located on the right side of the corridor.