At 9 mths LOs are still babies but they are also smart. They learn from their experiences and because every nap at 30-45 mins your wife steps in and bf to sleep your LO has 'learnt' that he needs to cry for that long to get what he needs to sleep. Does that make sense?
and
It could well be that, but in all honesty there is a lot of screaming usually hard screaming, would your wife consider carrying on with soothing LO rather than feeding him?
This will be key to this whole process.
Hang in there, you have had some GREAT input here, don't give up!