When the gangster approaches Harry he has his sleeves rolled up, with the bandage visible on his right arm. You also get to see the tattoo on his right hand several times.
After the shooting, the ‘gangster’ is stood up with this jacket sleeves rolled down. And when he lights the match there is no tattoo on his hand. You don’t see his face again.
I reckon Harry somehow overpowered the gangster and was able to swap the clothes etc over (not sure how, must knock him out somehow, although there is time – Leo only arrives as the first shot is fired), presumably with the intention of making the police think he was dead. Given that it was the same bloke who killed his misses that would be added incentive.