I’m no expert on your climate though can tell you blackberries should be transplanted when dormant. There are a few things I would do to reduce risks such as cut back the top to a few inches above the ground, leave the dirt at the location and move them barefoot. Give the roots a good rinse in water. Give the top a good spraying or dipping with an antifungal such as captan. An expert in your area may have other or better advice more relevant to your area. You can edit your title to get there attention to say something like " How and When do I propagate blackberries in North California". The advice I gave you works great in Kansas but California has different rules , regulations, pests, growing conditions etc.
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