There are a few things that need to be considered.
First, if he has a bouncy stride, this lessens his accomplishment (+6 seconds).
Second, types of shoe is important. If he had trainers on this would be impressive(-5.5 seconds). Flats would give the same conversion as actually racing the mile. Spikes would also lessen his accomplishment (+3.2 seconds).
Third, what was the temperature like in the gym? Did he have a fan to cool him (+4 seconds) or was it in a brutally hot gym (-2.5 seconds)?
Lastly, of course a treadmill is slower at no incline, because there is no wind resistance, so a uniform 10 seconds will be taken off of all times.
Based on the things above here are a couple of conversions.
All worse case scenarios (bouncy stride, spikes, fan) :
4:13 -> 4:36.2
Best case scenario (trainers, hot gym):
4:13 -> 4:15
I'm going to go for:
4:15-436.2
4:29