Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Consider the free-body diagram for block A. The force from the hand $F$ and the tension $T$ are the two horizontal forces acting on block A. Since block A accelerates in the direction of the hand's force $F$, then $F$ must be greater in magnitude then $T.$ Note that $T$ is the force of the string on block B. Therefore, the force of the string on block B is smaller than the force of the hand on A.