just be freaking thankful the deer ran that way towards your buddy and not the other direction. Hind quarter shot...however lethal you may think...is a serious injury and if the blood clots...the deer can suffer and die from infection. At least this deer was taken care of by your buddy...and since you did put a shot...the first "lethal" shot on a deer is classified as the taker...meaning the one who put the lethal shot in the deer is the one who gets to tag the deer. Consider yourself lucky....yea...he killed a deer you already shot...but you have deer in the freezer already...and you made a bad shot and your buddy captitalized on it. Congradulate him on a good shot...and thank him. Figure it this way...you still have a tag....and you got to shoot your gun!
the deer also could have taken off into another property and died...or could have ran 2 miles before it expired. Count your blessings....and your bro had every right to tag the deer....and you shouldnt have been waiting for him to ask to share....he killed it...its his.