Solution to the operator equations in Hilbert $C^*$-module

In this note we give necessary and sufficient conditions for which the operator system $A_1X=C_1,~ XB_2=C_2$,\linebreak $A_3XA^*_3=C_3$ and $A_4XA^*_4=C_4$ has common positive solution, where $A_i, C_i$ and $B_2$ are adjointable operators on Hilbert $C^*-$ modules.