Is it the case that all changes in phenotype during life are not inheritable?
The assertion "You cannot change in life what will be genetically inherited in any possible way" is true, as you cannot (healthily) change the DNA in your germ cells.

However, the assertion "You cannot change in life what will be inherited in any possible way" is wrong, because of epigenetics. Parts of your DNA are marked (in different ways), and this can be inherited and have an effect. E.g. the only causal difference between these two mice is the diet of their mothers:



Image source and a further explanation: Nutrition and the epigenome.