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

Let $L$ be some countable language and $M$ be an $L$-structure.
My question is:

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


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