Answer: I think you can safely move your hydrangea any time the ground is not frozen. I'd wait until after the first frost kills the leaves. The frost and dieback will prompt the plant to go into dormancy for the winter. Once it is dormant you can prune it back and move it without problem. If you prune it back while the leaves are still green, the stems may try to produce new foliage, which will be susceptible to winter weather. If you can wait until mid or late fall, the plant will be dormant and will not produce new growth after being pruned.
Best wishes with your hydrangea!
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