  We compute the conjugate system of twisted Araki-Woods von Neumann algebras $
\mathcal{L}_T(H) $ for a compatible braided crossing symmetric twist $T$ on a
finite dimensional Hilbert space $ \mathcal{H} $ with norm $ \|T\| <1$. This
implies that those algebras have finite non-microstates free Fisher information
and therefore are always factors of type $\text{III}_\lambda$ ($0<\lambda\leq
1$) or $ \text{II}_1 $. Moreover, using the nontracial free monotone transport,
we show that $ \mathcal{L}_T(H) $ is isomorphic to the free Araki-Woods algebra
$ \mathcal{L}_0(H) $ when $ \|T\|=q $ is small enough.
