Given 2 symplectic embeddings $g_0$ and $g_1$ of a 4-ball of radius $r \leq 1$ into the 4-ball of radius 1 (all equipped with the standard symplectic form coming from $\mathbb{R}^4$), does there exist a diffeomorphism $\phi$ such that $\phi \circ g_0 = g_1$ ?

More generally given 2n symplectic embeddings $(g_1, ......, g_n)$ and $(g_1^\prime,......, g_n^\prime)$ of a 4-ball of radius $r$ does there exist a diffeomorphism $\phi$ such that $\phi \circ g_i = g_i^\prime ~ ~\forall i \in \{1,....n\}$.