The ball does not bounce back and nor does the wall move.
is physically impossible.
If you consider the ball alone as the system then momentum would not be conserved because an external force (impulse) acts on the ball which originates from the wall (+ Earth).
If you consider the ball and the wall & Earth as the system then momentum is conserved as no external forces will be acing and the final momentum will be carried by the ball and the wall and the Earth.
Thus not all the kinetic energy is converted to other forms of energy but the amount of kinetic energy carried by the ball and the wall and the Earth will be very much smaller than the kinetic energy carried by the ball before the collision.
You can think of the problem as the centre of mass of the system carrying the momentum and having a finite but very small amount of kinetic energy compared with the kinetic energy of the ball before the collision.
Nothing that happens during the collision will change the motion of the centre of mass of the system because there are no external forces acting on the system.
The kinetic energy of the components of the system in the centre of mass frame can change.
The kinetic will not change if the collision is elastic, it could increase if there was an explosion when the ball impacted on the wall and that would be called a super-elastic collision.
In the case that you have asked about when the collision is inelastic the extreme of kinetic energy decrease would be that all the kinetic energy in the centre of mass frame is converted into other forms of energy ie in the centre of mass frame all the system components would be stationary.
Some of the kinetic energy is converted into heat by the collision causing the ball and the wall to vibrate.
Eventually all these vibrations would dissipate and the thermal kinetic energy of the wall and the ball would be larger - they become hotter.
There will also be permanent deformation of the wall and ball which means that work has been done to permanently break the bonds between the molecules and the energy to that comes from the kinetic energy that the ball had before the collision.