Definition of $Λ^*: End(Ω(J))→End(Ω(C))$ from Abel Jacobi map $Λ$?

Question

Let $C$ be a hyper elliptic curve of genus $2$. Let $J(C)$ be its Jacobean. There is Abel Jacobi map $Λ:C→J(C)$.

Let $Ω(J)$ and $Ω(C)$ be space of holomorphic differential form on $J$ and $C$ respectively.

Then, how can we define $Λ^*: End(Ω(J))→End(Ω(C))$ naturally from $Λ$ ? Thank you for your help.

P.S : $Λ^*$ appears in $368p$ of https://www.ms.u-tokyo.ac.jp/journal/pdf/jms210205.pdf without no explanation.