Ми описуємо ін'єктивні ендоморфізми напівгрупи $\boldsymbol{B}_{\mathbb{Z}}^{\mathscr{F}^2}$ з двоелементною сім'єю  $\mathscr{F}^2$ індуктивних непорожніх підмножин у $\omega$. Зокрема, доводимо, що кожний ін'єктивний ендоморфізм $\mathfrak{e}$ напівгрупи  $\boldsymbol{B}_{Z\mathbb{}}^{\mathscr{F}^2}$ зображається у вигляді $\mathfrak{e}=\mathfrak{e}_0\mathfrak{a}$, де $\mathfrak{e}_0$ -- ін'єктивний $(0,0,[0))$-ендоморфізм  і $\mathfrak{a}$ -- автоморфізм $\mathfrak{a}$ напівгрупи $\boldsymbol{B}_{\mathbb{Z}}^{\mathscr{F}^2}$. Також ми описуємо усі ін'єктивні  $(0,0,[0))$-ендоморфізми $\mathfrak{e}_0$ напівгрупи $\boldsymbol{B}_{\mathbb{Z}}^{\mathscr{F}^2}$, тобто такі, що $(0,0,[0))\mathfrak{e}_0=(0,0,[0))$.

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