No one has answered so I will just suggest you treat it like any other hardy perennial and move it when you would move other HPs e.g daylilies etc. In my climate that could be any time after the plant has died down for winter but I don't know the recommendations for your area. The more leaf the plant has the less well it will transplant as it has a lot of transpiration going on which transplanted roots will have trouble supporting. On balance I would suggest you do it now before it produces any more growth.

It self seeds easily.

attached link has interesting information about how to propagate the tap root by cutting it in little pieces. Seriously, though, if you let your plant bloom and make some seeds you will have many little plants in short order without any trouble or expense --so many, in fact, that you might wish you had planted them in a space with more room for them to spread.

Here is a link that might be useful: propagating Myrrhis odorata (scroll down)

Uh, get rid of it as fast as you can. Some specimen made its way into my garden bed, and at first I enjoyed the flowers. It continued growing and is suffocating lilies, toad lilies and russian iris. It has a massive root that as far as I can tell goes down at least a 1.5 metres. I can't imagine why anyone would want this and why it's allowed to be sold in nurseries. From BC south coast, Canada.