A

Step 1: Identify the forces acting on the smaller block (mass m) and larger block (mass M). The force F is applied horizontally on mass m, which will create a frictional force between m and M, acting in the opposite direction of F.
Step 2: The frictional force (f) can be calculated using the formula: \( f = \mu N \), where N is the normal force on mass m caused by mass M. If we assume mass M exerts its weight fully onto mass m, then \( N = mg \). Hence, \( f = \mu mg \).
Step 3: The maximum frictional force must be overcome by force F for block m to move. Assuming static friction, the total horizontal force exerted by mass M against the wall will equal the applied force F minus the frictional force.
Step 4: By applying Newton's laws, we can express the equilibrium condition for masses M and m:
\( F - f = Ma \) (for mass m in horizontal direction)
Knowing that block m's acceleration affects M due to connection by friction, we can conclude:
The vertical wall must exert a normal force equaling the frictional force, hence the action-reaction force between m and M will be equivalent to \( f \).
Therefore, the value of action-reaction forces between m and M is equal to the frictional force calculated.
Therefore, the answer is A.