Not meaning to rain on your parade, but finding that exact, near 40 year old jacket, that would be a proper fit, is more like a needle in many haystacks. You could try contacting the Raiders front office and they might have some record as to who made the jacket in 1983. The city of Oakland might have some record of businesses active in 1983. I doubt either avenue mention will be of help.
I still suggest creating a search on ebay. Do a search for vintage Raiders jacket. Look through the many pages of hits I just found to see if you might find the jacket you want. Once you have gone through ever page of jackets and don't find a match, safe your search and have an email sent to you whenever a new ad is placed. I have had success finding some 70 year old tools I wanted. It didn't happen over night but it did happen.
I'm sure your friend would love to get his jacket back. Even if you find the same jacket... it will not be the one that's lost. He might have to settle for one that's similar or simply deal with his loss.
The last option, but I'm sure quite expensive, would be to take your pictures to a reputable tailor and have one made. I'm sure it can be reproduced... if money was no object.