The concept of a force lifting a weight and the work done

[A.T.]

Note that if one insists that the friction force does work,

You just apply the definition of work to both bodies (A, B) and the two equal but opposite friction forces acting on them.

it is not possible to explain where the energy is going.

For kinetic friction the work done by A on B is of different magnitude than the work done by B on A. That difference represents the energy dissipated as heat.