Question

what happens to the movement of molecules at equilibrium

Answer 1

the molecules at equilibrium move through the semi-permeable membrane back in forth but equally since equilibrium was reached already it just needs to keep it by keeping the movement of molecules going from one side of the membrane to the other equal.

Answer 2

Are you talking of internal movement ? it would then fluctuate around that equilibrium like harmonic oscilators for small molecules.
If you are talking of the movement of molecules in a given space it would move randomly but the net movement would be nul (as stated above)