CIO doesn't work for all babies, just the ones that give up after 10 minutes. We never really tried CIO on purpose, but on a road trip or two, ended up doing it. I'm talking 45 minutes to 1 hour straight of crying, no signs of slowing down or stopping. Pretty sure she'd have gone on longer if we hadn't intervened.
Nursing to sleep is something babies love to do, but it's definitely a bad habit to have. Obviously because it can infringe upon mom's needs, and create a dependency to get to sleep for baby. Also, I know a mom that let her babies nurse to sleep all the time, and was also an extended nurser. She ended up having to have two decaying baby teeth pulled on her toddler. Now, the doctor said it was due to night nursing, but she thinks otherwise. I am not a doctor, nor was I the mom that was there 24/7 to know what really went on, but that was the doctor's explanation.
But I don't believe in CIO. I do believe in pick up/put down. This can take a while, and if you Dad can do it instead of Mom, it can be more successful. So when baby cries after being put down, mom or dad picks baby up to comfort, but doesn't feed. When baby is calm, put him back down. You can even stay at the crib for a moment with your hand on baby. I think letting your baby know you are there to meet his needs is a good thing. So long as your needs are not going unmet because of baby.
Another thing she can try is to go ahead and nurse him but don't let him fall asleep at the breast. Give his feet a tickle or something to keep him up, and unlatch him when he is just short of sleeping to put him down. If you get the timing just right, he'll be hitting the mattress just barely cognizant that he's being put down w/o being nursed to sleep completely. If he wakes after this, do the pick up put down. I think PUPD is from the baby whisperer or something. Not my most favorite resources, but decent, and a lot more middle of the road and flexible than books that I think should be titled "how to make your baby hate you and life."
IDK what time you are putting him down, but I used to put my babies down at 8 pm, and then I'd wake them just enough to nurse for a bit right before I went to bed at around 11. Some people call this the dream feed. This would top babe off and get us through till a reasonable hour (6 or later) in the morning.
My favorite sleep book was the "no-cry sleep solution" by Elizabeth Pantley. My kids weren't horrible sleepers, but I read at least 10 books about babies and sleep cover to cover before my 1st was even 9 months old.
Good luck. Babies are tough. Kids are harder and easier in different ways. It's a journey, but such is life!