Let $\mathfrak{M}$ be a countable transitive model of set theory.

Let $L$ be some countable language and $A$ be a countable (in $\mathfrak{M}$) $L$-structure. My question is:

In $\mathfrak{M}$ can we carry the construction of Scott sentence of $A$ $\sigma(A)^\mathfrak{M}$?

Is $\sigma(A)^\mathfrak{M}$ identical with the Scott sentence of $A$ in the real world?