How to use ALE for moving boundary problems?

Dear Mr.Dokken

https://fenicsproject.discourse.group/t/moving-mesh-causes-entangled-cells/4159

Can we do the same thing in FunctionSpace as well?(not vector function space like the example above) What I want to do is to compute the numerical solution u(x,y) with original mesh(star in center) at time=0, and then move the star a bit to the right side and compute the numerical solution u(x,y), like this.
How can I move the star from the center to anywhere?