What is the status of Ihara's lemma for Shimura curves over totally real fields? In particular, why is it not implicit in the exact sequence of Rajaei, "On the levels of mod $l$ Hilbert modular forms" (Crelle 2001), Theorem 3 (3.18)?

To be a little bit more precise (or at least to give the main idea), let $F$ be a totally real field of degree $d$. Let $M(\mathfrak{M}^+, \mathfrak{M}^{-})$ be the Shimura curve of level $\mathfrak{M}^+ \subset \mathcal{O}_F$ associated to the indefinite quaternion algebra of discriminant $\mathfrak{M}^{-} \subset \mathcal{O}_F$, and $M(\mathfrak{m};\mathfrak{M}^+, \mathfrak{M}^{-})$ the Shimura curve with maximal level at primes dividing $\mathfrak{m} \subset \mathcal{O}_F$. Fix two coprime ideals $\mathfrak{N}^+, \mathfrak{N}^{-} \subset \mathcal{O}_F$ such that $\mathfrak{N}^{-}$ is the squarefree product of a number of primes ideals congruent to $d \mod 2$. Suppose that $\mathfrak{N}^{-}$ has at least one prime divisor $\mathfrak{q}$ say. Fix a prime $v \subset \mathcal{O}_F$ that does not divide $\mathfrak{N}^+\mathfrak{N}^{-}$. Let ${\bf{M}}(\mathfrak{q}; \mathfrak{N}^+, \mathfrak{N}/\mathfrak{q})$ and ${\bf{M}}(v\mathfrak{q}; \mathfrak{N}^+, \mathfrak{N}^{-}/\mathfrak{q})$ be the good reduction integral models over $\mathcal{O}_{(\mathfrak{q})}$ of $\bf{M}(\mathfrak{q}; \mathfrak{N}^+, \mathfrak{N}/\mathfrak{q})$ and $M(v\mathfrak{q}; \mathfrak{N}^+, \mathfrak{N}^{-}/\mathfrak{q})$ respectively. Ihara's lemma for Shimura curves over totally real fields, at least as I understand it, is the assertion that for any non-Eisenstein maximal ideal $\mathfrak{m}$ in the algebra $\mathbb{T}(v\mathfrak{q}; \mathfrak{N}^+, \mathfrak{N}^{-})$ generated by Hecke operators acting on $M(v\mathfrak{q}; \mathfrak{N}^+, \mathfrak{N}^{-}/\mathfrak{q})$, the map \begin{align*} H^1({\bf{M}}(\mathfrak{q}; \mathfrak{N}^+, \mathfrak{N}/\mathfrak{q}), \mathcal{F})_{\mathfrak{m}}^{2} &\longrightarrow H^1({\bf{M}}(v\mathfrak{q}; \mathfrak{N}^+, \mathfrak{N}^{-}/\mathfrak{q}), \mathcal{F})_{\mathfrak{m}} \\ (f_1, f_2) &\longmapsto 1_* f_1 +\eta_{v, *} f_2 \end{align*} is injective, where $\eta_v = \left( \begin{array}{cccc} 1 & 0 \\ 0 & \pi_v \end{array}\right)$. Here, $\mathcal{F}$ is the usual sheaf defined by Carayol and Jarvis, and $\pi_v$ is a fixed uniformizer at $v$. Rajaei shows that there is an injection of the associated dual character groups, \begin{align*} \widehat{\mathcal{X}}_{\mathfrak{q}}(\mathfrak{q}; \mathfrak{N}^+, \mathfrak{N}/\mathfrak{q}))_{\mathfrak{m}}^{2} &\longrightarrow \widehat{\mathcal{X}}_{\mathfrak{q}}(v\mathfrak{q}; \mathfrak{N}^+, \mathfrak{N}^{-}/\mathfrak{q})_{\mathfrak{m}} \\(f_1, f_2) &\longmapsto 1_* f_1 +\eta_{v, *} f_2 .\end{align*} Sorry if the question is naive!