This is my first try ever with this, I guess the best way to tell if it worked is if the teeth were cut without injuring the puffer. I’ve seen some horror stories where the lips get cut up. The puffer is swimming around like norma now, so I guess it went well. Usually you want to get the teeth as short as possible so it takes as long as possible before they grow back.
The teeth are similar to rodents or to a bird’s beak. It continuously grows, so hard foods are necessary to keep it ground down. For most species of pufferfish, the beaks can be kept well trimmed by regular feedings of hard shelled inverts: snails, crabs, clams, shrimp, crayfish, even insects, replicating their natural diets.
For some species, notably amazons and avocado puffers, their beaks grow extra fast and not even the hard food diet is enough, and routine dentistry becomes needed.
Considering both amazons and avocados are riverine species, my theory (and this is purely speculative) is that they also use a lot of energy and metabolize fast (I have noticed that the amazons look back to normal pretty fast after feeding - the bellies will swell after large meals), thus needing lots of food. To compensate for the more frequent, hard shelled foods, the teeth may have evolved to grow faster and keep up. I doubt there’s any research with that though.