Sorry to answer a question with a question but would it be easier to take cuttings? It may be worth considering even if you decide to go ahead and move the original, you could have several replacements to choose from if the move doesn't go to plan.

I've done it.
I'd water it well first to soften the soil round it to help you get as much rootball out as possible.
Get the hole it's going into ready before you start to dig the honeysuckle up. Fill that hole with water and let it drain away so that it goes into moist soil.
I'd recommend pruning the plant back to reduce strain on the roots and to help disentangle it from whatever it's growing up now.
Dig up the plant, taking as much of its root system and the soil around it as you can.
Plant it in the new situation, matching soil levels, and make a little wall about 2 feet in diameter out of soil (an inch or two high) around the plant to help keep water in the area over the honeysuckle's roots when you water it.
Water thoroughly immediately after planting.
You may need to help the plant find its support by twiddling the remaining stems round whatever you want it to grow over - trellis, netting, whatever.
You'll need to make sure this plant is kept watered until it is established - could be for a year or so. It will need at least a bucketful of water at a time, poured on slowly so it can soak into the soil and not run away.

Xela's suggestion of cuttings would give you insurance - do both!

Thanks for the advice, will defo go with the cuttings before moving the plant.