The law of conservation of momentum states that for two objects colliding in an isolated system, the total momentum before and after the collision is equal. This is because the momentum lost by one object is equal to the momentum gained by the other.
What is essential condition for the validity of law of conservation of momentum?
The only condition is that there are no other forces acting on the system. A force is equal to some change in momentum per unit time. So if a force is exerted, momentum is added to (or subtracted from) the system.