Showing a full screen dialog to view a full list of radio button selection

I'm designing a sort of step by step process for mobile web using a stepper to get a bunch of information from a user. One of the steps requires a user to select from a list of (about 20) pre-defined locations or enter their own address (entering their own is not high priority).

Since the stepper and the list of locations can get really long, I am having the user launch a modal to view all the choices in a full screen dialog so that they don't have to scroll the stepper to select a location.

The problem however is that after selecting a location (with a radio button) on the modal and closing it, how to show in the wizard what they have selected in the modal after the modal is closed.

Does anybody have an idea? Is launching the modal even a good idea?