Consider Complex torus $ {C}/L$ , with quotient map $ \pi : C \rightarrow C/L$ . Let $ f: C/L \rightarrow C$ be a Complex valued function . Then $f $ is holomorphic at $p \in C/L$ if and only if there is a preimage $z$ of $p\in C$ such that $f \circ \pi$ is holomorphic at $z$ .
// I have done one side of the proof if f is holomorphic then $f \circ \pi$ is holomorphic. Because on $C/L$ we have the charts $\phi_{z_0}= \pi^{-1}|_{D(z_{0},r)}$ where r>0 is a positive real number such that $\mod(w)>2r $ for all $w\in L$. (Algebraic curves and Riemann surfaces by Rick Miranda page 9). So using this chart I will show that $f\circ \pi$ is holomorphic. How to show the converse part ?