Consimilarity and quaternion matrix equations $AX-\widehat{X}B=C$, $X-A\widehat{X}B=C$

L.Huang [Linear Algebra Appl. 331 (2001) 21-30] gave a canonical form of a quaternion matrix $A$ with respect to consimilarity transformations ${\tilde{S}}^{-1}AS$ in which $S$ is a nonsingular quaternion matrix and $\tilde{h}:=a-bi+cj-dk$ for each quaternion $h=a+bi+cj+dk$. We give an analogous canonical form of a quaternion matrix with respect to consimilarity transformations ${\widehat{S}}^{-1}AS$ in which $h\mapsto \widehat{h}$ is an arbitrary involutive automorphism of the skew field of quaternions. We apply the obtained canonical form to the quaternion matrix equations $AX-\widehat{X}B=C$ and $X-A\widehat{X}B=C$.