  In this paper we study the partial Brauer $\mathbb{C}$-algebras
$\mathfrak{R}_n(\delta,\delta')$, where $n \in \mathbb{N}$ and
$\delta,\delta'\in\mathbb{C}$. We show that these algebras are generically
semisimple, construct the Specht modules and determine the Specht module
restriction rules for the restriction $\mathfrak{R}_{n-1} \hookrightarrow
\mathfrak{R}_n$. We also determine the corresponding decomposition matrix, and
the Cartan decomposition matrix.
