Logarithmic Cartan geometry on complex manifolds with trivial logarithmic tangent bundle

Let $M$ be a compact complex manifold, and $D\subset M$ a reduced normal crossing divisor on it, such that the logarithmic tangent bundle $TM(-\log D)$ is holomorphically trivial. Let $\mathbb{A}$ denote the maximal connected subgroup of the group of all holomorphic automorphisms of $M$ that preserve the divisor $D$. Take a holomorphic Cartan geometry $(E_H,\mathrm{\Theta })$ of type $(G,H)$ on $M$, where $H\subset G$ are complex Lie groups. We prove that $(E_H,\mathrm{\Theta })$ is isomorphic to $({\rho }^{\ast }{E}_H,{\rho }^{\ast }\mathrm{\Theta })$ for every $\rho \in \mathbb{A}$ if and only if the principal $H$–bundle $E_H$ admits a logarithmic connection $\mathrm{\Delta }$ singular on $D$ such that $\mathrm{\Theta }$ is preserved by the connection $\mathrm{\Delta }$.