$\DeclareMathOperator\Aut{Aut}$Let $X$ and $Y$ be SFT and $X\subset Y$, and $\phi:X\rightarrow X$ be a homeomorphism commuting with the shift map. Is there any extension of $\phi$ on $Y$ whic is a homeomorphism and commuting with shift?  (Is $\Aut(X)\subset \Aut(Y)$?)