It is during prophase of mitosis when the DNA condense and nucleus dissolves, the dissolve of the nuclear membrane signals the prometaphse of mitosis.
But that is only based on the university level, in high school level, we classify all nuclear membrane, nucleolus and nucleus dissolve during prophase of mitosis.
Explanation: Mutations can only be passed down if the mutation happens in reproductive cells. Egg cells are reproductive cells. (Along with sperm in males.)