Answer: Yes you can transplant them in the fall, although spring (late March to April) would be better. You did not mention which type of raspberries you had. Some form a hedgerow while others tend to remain individual plants. Hedgerow types should have canes about 6 - 8 inches apart after pruning or digging. Individual plants should have 5 or 6 canes left.
Cut the canes on the plants you dig up back to about 8 inches long. This stub can be used as a "handle" to assist in transplanting them in their new location.
Good luck with those berries!
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