M5766 Update #21:00 AM
A back stay is a layer of fabric that is loose across the upper back, but caught in the neck, shoulder, armhole, and underarm seams. It acts as a buffer between the shoulder pads and the fashion fabric. It also adds strength across the back when you reach and supports the jacket when stored on a hanger. You can use any firmly woven sew-in interfacing such as Armo Press or a quilt cotton or muslin. I used muslin.
Source: Jackets For Real People
Next, I'll add the lining...