Honeysuckle is an easy woody vine to transplant, or even to take cuttings. If you are ambitious enough, you can cut it 3' off of the ground and take your cuttings and put them in a good potting mix watered in with a liquid Root Tone mix (indole 3 butyric acid). Most of the cuttings will root if you keep them watered enough. Then you still have your 3' tangle of woody vine left that you can dig up and transplant. Take it to your house and transplant it, it will make a good mother for other cuttings if you have friends or neighbors that would like some (or customers). If you can leave some foliage, it will adjust to the transplanting much faster. The optimum time to transplant it will be in the fall, but it is very hardy and should transplant successfully, even in the heat of summer provided you give it plenty of water. Don't let it completely dry out for at least 8 weeks.