Positivеly prime models over a normal basic set

For given universal domain $C$, a set $\mathrm{BF}$ of normal formulas, and $A\subseteq C$, we construct substructures $B$ of $C$ with the following properties: (a) $A\subseteq B$; (b) for each $a\in B$ the type ${\rm tp}(a;(B\setminus\{a\}))$ is based by formulas from $\mathrm{BF}$. The existence and uniqueness theorems are proven. This is a generalization of the known results on the injective hulls in the variety of the modules in case when the theory $\mathrm{Th}(C^\omega)$ is stable.