Mirror an object's movement/rotation/scale but on different orientation

Question

So I want to move/rotate/scale two objects with exactly the same value but in different orientation. If I just parent object A to Object B then the transforms are the same and child object inherits the orientation of parent, but I want when I move parent the child to inherit the values but on it's own orientation.

So I move parent 5m on X , child to move 5m on "it's" X which is different than of parent.

I hope that makes sense :)