If $u$ is in fiber under given group homomorphism then where is $u^{-1}$?

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Suppose we have $\phi: G \to H$ is a group homomorphism, s.t. $\phi^{-1}(a)=X \in G/K$ for some $a\in H$, and $K=\ker\phi$. If $u$ is in fiber under $\phi$ can we determine where is $u^{-1}$?