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Although they are hardy, (assuming it's a hardy fuchsia), they are sometimes a bit borderline, so I wouldn't want to move it now, so late into autumn. It might not have enough of a chance to settle itself before hard frosts and could suffer a bit. I'd move it in early spring when the worst of the cold is past.
You could cut it back a bit at the same time so the newly re-growing roots have less foliage to support.
Also a good opportunity to improve the new planting hole a bit with some compost/manure and maybe sprinkle some mychorrizal fungi to help the roots out.
I've got a fuchsia that has started to grow bigger than expected so thinking of shifting it to a different spot in the bed. When's the best time to do this and is there anything I should be doing apart from just digging it up in one place and sticking it in a hole in another.