I would get rid of the battery or replace it with a fake. I have an old iPhone 3GS that was basically sitting around for many years at zero charge and was kind of confused to find the Otterbox case popping open when I dug it up one day. Opened up the Otterbox to find the rear of it had swelled considerably. It's not like it spontaneously combusted on me or anything, and it's still fine, but since you're framing this and it could fall down randomly or something when the battery is old and maybe swells, I wouldn't take the risk.