The secret is in winding up the left shoulder for the punch, but without turning the whole torso around. You have to step on it. All these "right off the bat" hooks will bring damage to your shoulder over time. If you must do it (to catch someone coming in) give yourself some room. What I mean is, let your left leg slide to the left when you start the hook, so you dip down a bit. You can pressure the shoulder more on the turn then, because there's some force (from the dip) that is being generated instead of it all coming from the shoulder (well, from the core obviously, but you get my drift).
But in general, left hook (power left hook) should come after a good right straight, so that your body is already positioned and twisted for it. The longer the hand travels, the stronger the punch.
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Here from 3:31, Anderson shows it, it's the best video I could find in short time that shows it right. Only personally, I don't twist the fist, I leave the palm facing me but that's a debatable issue best left for some other time.
BTW, I hope you are killing chin-ups and 30 sec to a minute static chin-up holds. If not, your shoulder will go out in time anyway. Lots of stretching and this and you'll be fine.