unless he was traveling for over 2 days, i dont think it was NH3 poisoning. honestly, bettas are particularly resilient to NH3 and NO2, likely in part due to having really sh*tty gills (which is where these toxins enter the fish).
and they tend to be hardy with acclimation too.
if he died a week later, i would bet parasites. fish can live with parasites for years without any symptoms, but after a major stressor (like shipping) they cant handle the parasite load anymore and die.
what i do when i ship bettas, is put a drop of Prime in the bag. it binds out NH3 for 24-48 hours, so usually there is 0 NH3 when the fish arrives. i will also add a drop upon first opening a bag of a fish shipped to me, to neutralize any NH3 that may have accumulated so the poisoning stops instantly, and not 40 min later when i finish acclimating.
Oh? Maybe that is why he was so small compared to his spawn sisters?!? Parasites.