During an elastic collision,

In an elastic collision, the total linear momentum of the system is conserved at every instant because no external impulsive forces act on the system. Thus, the linear momentum stays constant throughout the process, which also implies that the final linear momentum equals the initial linear momentum.

During the actual time of contact (deformation phase), a part of the kinetic energy is temporarily converted into elastic potential energy. Therefore, the kinetic energy does not stay constant during the collision. However, after the bodies separate, this potential energy is completely converted back into kinetic energy. Thus, the final kinetic energy equals the initial kinetic energy.

Hence, the final kinetic energy equals the initial kinetic energy, the final linear momentum equals the initial linear momentum, and the linear momentum stays constant.