Infinitely many divisibility instances for the generalized recurrence sequence $b_T$

Let $L=(1,-1)$, let $K$ be the parameter appearing in the definition of the generalized sequence $b_T$, and let $h\in\mathbb{N}$. Infinitely-many-instances conjecture for $b_T$. If $\operatorname{\underline{\deg}} K\geq 2$ and there exists $n_{1}$ such that $h$ divides $b_T(n_{1})$, then there exist infinitely many numbers $n$ such that $h$ divides $b_T(n)$. The conjecture is connected in the source with the preceding theorem and is presented as open.