If B and C had the same angular momentum $(L_B=L_C)$ then at point 1 we would have $m_Bv_Br_B=m_Cv_Cr_C$.
We are told that $m_B=m_C$. Since B and C are at the same position then $r_B=r_C$. Therefore we must also have $v_B=v_C$.
However, if this were the case then B and C would follow the same orbit at point 1. Instead they follow different orbits. So we must have $v_B \gt v_C$. It cannot be true that $L_B=L_C$.