Well I am in the UK so ymmv, but yep, I am just about to plant out my caryopteris clandonensis. In fact, autumn is my major planting season for pretty much everything, on the principle that the soil is still warm but winter rains will aid in root establishment...whereas spring plantings always need substantial supplementary irrigation.

you should know by now.. that you dont need special rules for every plant. ..

all perennials can be moved in dormancy ... that means fall or spring ... and for many.. all winter long... except for those of us in ground freeze .. which by the way.. you could move them.. if you happen to have a pick ax.... and want to work outside in below zero temps.... thats F for you C peeps.. lol ...

sooo.. find a new spot... dig an approximate hole .. about one shovel deep ... go harvest the plant.. digging a root mass about one shovel deep.. hoik it across the yard.. and throw it in the hole.. and back fill the rest.. then go fill the other hole ...

i laid it ALL out.. just in case you were looking for that special rule ...

in spring.. we want it done 6 to 8 weeks before the heat of summer.. in fall we want it done 6 to 8 weeks before the ground freezes ..

remember.. a dormant plant has no reason to waste or lose leaves... since the plant is dormant..

up to you whether you want to cut it back severely.. leave it for spring.. so yo know where the plant is.. and it will be a bit of self mulching for the plant ...

water in properly.l. just once.. deeply.. and sin e its fall.. that will probably be all the watering it needs until late spring ... but in case of fall drought.. go out and check around thxgvg.. and give it a drink iof its some dry ...

ken

ps: one caveat.. in ground freeze ... small plants might heave in late winter .. leave those to move in spring ....yours does not appear small. unless you plan on dividing it too much ...

You may lose this year’s blooms. As floral and Ken said, transplant now, the sooner the better so the roots can settle in and grow. Mulch over the roots but leave some space around the stems. Mulch will reduce freeze-thaw cycles and reduce the chance of frost heaving.

Yours is probably rotting off and not likely to bounce back from simply being moved - these need open situations with sandy or otherwise well aerated soil.