Yes, cable has no problem. In fact we tried to move the lever on the caliper itself and didn't see it pushed the piston.Are you sure that the inner cable slides freely? They sometimes corrode inside and "stick". Easy to check, have someone operate and watch the cable at the brake end.
Probably previous owner's mechanic did that. When I received this car, both hand brake cables (L+R) were disconnected, and reason given to me because "it typically jammed"...Another possibility is that it just needs lubricating. The plastic cap at the pivot of the lever is easy to pop off and get in with some penetrating oil if necessary, and moly grease afterwards.
But if somebody has damaged the handbrake mechanism (typically by pushing the piston back mechanically) then you'll need to replace it. Sorry, can't help with that. Make sure that anyone working on the brakes in future knows about giving the piston a quarter turn so it can be pushed in.
Have fun,
Rob.