if it was a lost badge and the dt was still mos, then he would have had to report the loss and fillout tons of paperwork. when I was a nyc peace officer,that's what happened to my partner when his shield went mia.
on the other hand, when we needed police uniforms, etc for a production we were doing, I sent one of our theatre guys- a 65 year old harmeless looking guy into a pd supply shop and he had no trouble buying a matching # hat insignia and real shield that cop #xxxx failed to pick up.
I personally wouldn't report this badge...would raise too many questions of its provenance...and this could go from nypd to doi...not fun.
mp