Let $V$ be a $2m$-dimensional symplectic space over an infinite field $K$. Let $\mathfrak{ B}^{ (f)}_{ n,K}$ be the two-sided ideal of the Birman--Murakami--Wenzl algebra $\mathfrak{ B}_{ n,K}$ generated by $E_1E_3\cdots E_{ 2f-1}$ with $1\leq f\leq\left\lfloor \frac n2 \right\rfloor$. In this paper, using the diagram category of framed tangles and canonical basis, we prove that the natural homomorphism from $\mathfrak{ B}_{ n,K}/\mathfrak{ B}^{ (f)}_{ n,K}$ to $ \mathrm{ End}_{ U_q(\mathfrak{ sp}_{ 2m})}\left(V^{ \otimes n}/\left(V^{ \otimes n}\cdot \mathfrak{ B}^{ (f)}_{ n,K}\right)\right)$ is always surjective.
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