when all the top growth has turned yellow/brown cut it right back & then it will be fine to lift/divide crowns. Remember to spread roots out in a fan shape if possible when planting. Also make sure there is a top bud/node per division for next years leaf growth.

So far as I know there isn't a 'best time' you just go ahead and split into two.

Sudden thought are you asking about the decorative house plant Asparagus Fern or asparagus that you grow for eating. if the later the Bizzyb is correct.

Oh!! well spotted MG, that never occured to me !! Like my Grandma wisely used to say " Presumption is not knowledge"

Thank you for your quick replies. It is an outside asparagus - one you can eat only I leave it for the fern foliage. I will wait for it to die back before trying to divide it.