We give a complete classification of right coideal subalgebras that contain all grouplike elements for the quantum group $U_q^{+}\left({\mathrm{𝔰𝔬}}_{2n+1}\right)$ provided that $q$ is not a root of 1. If $q$ has a finite multiplicative order $t>4$; this classification remains valid for homogeneous right coideal subalgebras of the Frobenius–Lusztig kernel $u_q^{+}\left({\mathrm{𝔰𝔬}}_{2n+1}\right)$. In particular, the total number of right coideal subalgebras that contain the coradical equals $\left(2n\right)!!$; the order of the Weyl group defined by the root system of type $B_n$.