Question: how to transplant plants without killing them?
Answer: If you are able, choose the season you move.
Mark where everything is going to go first.
Pot, bucket or burlap: get the transportation ready.
Use a special watering schedule for soon to be in-transit plants.
Trim excess stems.
Dig up using the drip line.
Re-plant (the right way).
Reduce stress on the plants.