Although front squats and back squats develop tremendous lower body and overall body stabilizing strength, each one has slight mechanical differences which, in my opinion, will not allow one to improve the other.
Becuase the load is held in front of the body, front squats place a lot of work on the core and spinal musculature.
Your upper body angle is approximately 60-80 degrees of foward flexion which helps to keep you from falling foward! Also, load placement being in front places a little more of the stress on the quadriceps, but as with all squats depth dictactes what muscle groups contributes more or less to the execution of the movement.
Back Squats require good stabilizing strength of the external rotators of the shoulder, scapular retractors, scapular adductors, latissimus dorsi in conjunction with the spinal musculature, and core. Back Squats places your body approximately 45-50 degrees of foward flexion which really stresses the spinal-glute musculature.
So, in my opinion carry-over of one exercise to another of similiar mechanics such as these exercises can have similiar muscle adaptations but i can not see the carry-over being similiar as far as mechanics and muscle group activation for stabilization and movement pattern.