Weak-local triple derivations on C*-algebras and JB*-triples

We prove that every weak-local triple derivation on a JB$^*$-triple $E$ (i.e. a linear map $T: E\to E$ such that for each $φ\in E^*$ and each $a\in E$, there exists a triple derivation $δ_{a,φ} : E\to E$, depending on $φ$ and $a$, such that $φT(a) = φδ_{a,φ} (a)$) is a (continuous) triple derivation.