She could just continue to offer a cup. 4 month olds can become pretty 
skilled with the cup. I've sometimes had success with the mini Haberman 
feeder for babies with exquisitely sensitive gag reflexes. The teat is 
short and does not seem to stimulate the gaggy spot of the palate, and 
the flow is controllable. Those high palates are generally caused by 
restricted tongue movements, from either tongue tie or a short lower jaw 
(in a healthy child, many genetic disorders also feature high, very 
unusually shaped palates).
Catherine Watson Genna, IBCLC  NYC

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