$\DeclareMathOperator\Aut{Aut}$Let $X$ and $Y$ be two subshifts of finite type and $X\subset Y$, and $\phi:X\rightarrow X$ be a homeomorphism commuting with the shift map. Is there any homeomorphism $\tilde{\phi}:Y\rightarrow Y$ on $Y$ commuting with the shift map and $\tilde{\phi}|_X=\phi$?

$\DeclareMathOperator\Aut{Aut}$Let $X$ and $Y$ be two subshifts of finite type and $X\subset Y$, and $\phi:X\rightarrow X$ be a homeomorphism commuting with the shift map. Is there any homeomorphism $\tilde{\phi}:Y\rightarrow Y$ commuting with the shift map such that $\tilde{\phi}|_X=\phi$?

$\DeclareMathOperator\Aut{Aut}$Let $X$ and $Y$ be two subshift of finite type and $X\subset Y$, and $\phi:X\rightarrow X$ be a homeomorphism commuting with the shift map. Is there any homeomorphism $\tilde{\phi}:Y\rightarrow Y$ on $Y$ commuting with the shift map and $\tilde{\phi}|_X=\phi$?

$\DeclareMathOperator\Aut{Aut}$Let $X$ and $Y$ be two subshifts of finite type and $X\subset Y$, and $\phi:X\rightarrow X$ be a homeomorphism commuting with the shift map. Is there any homeomorphism $\tilde{\phi}:Y\rightarrow Y$ on $Y$ commuting with the shift map and $\tilde{\phi}|_X=\phi$?