I never moved mine in a previous garden. I think eventually it was in a similar situation as yours and simply disappeared.

In any case, I would suggest moving in the spring when new growth begins to emerge.

FYI, I planted 'Sandrine' this spring, which is very similar but more vigourous and with larger flowers -- I love it so far.

I think this is one that doesn't like to be moved. I would follow "coolplantsguy's" suggestion of transplanting it in the spring. Take as much soil around the root as you can and dig carefully to get as much root as possible. If it does die, then that is an excuse to visit a nursery to purchase another one. I've had a couple of Ann Folkards that just died out from being too crowded and shaded by other plants. Another one I have in more sun just blooms all summer. I couldn't resist and just got another Ann Folkard recently in a half-price sale, so must get it planted.