There is common courtesy and then there is the law.
ALL of the CO DOW regulations use the word "kill" for tagging, use of meat, etc. The actual legal right to an animal is to the person who "killed" the animal. If it was alive and then finished off with a subsequent shot, the kill shot claims possession.
There is some gray area. If your shot "would" have killed it, there is obviously a potential claim. Based on the description, I would say that the kill shot of your friend would obligate him to tag the animal. The proper thing to do (IMHO) would be to share the meat unless your wife ended up filling her tag. Then your friend should at least thank her with the backstraps.
Be careful of the regulations on party hunting. If your friend's shot was viewed as the "kill" shot by a DOW officer, but it had your wife's tag on it, they could potentially take the carcass and issue two tickets for party hunting.
Go read the regs..."kill" is the operative word.