Inductive blockwise Alperin weight condition for type B and odd primes

By the reduction theorems of Navarro–Tiep and Sp"ath, a way to prove the Alperin weight conjecture and its blockwise version is to verify the co-called inductive Alperin weight condition and inductive blockwise Alperin weight condition for all finie simple groups respectively. In this paper, we establish the inductive blockwise Alperin weight condition for simple groups of type $\mathsf{B}$ and odd primes, using a criterion given by Brough and Sp"ath recently.