Oriental poppies are best propagated by root cuttings.

Oriental poppies need at least eight hours of bright sunlight each day to produce the best blooms. Oriental poppies are one of my favorite garden flowers, because they’re just over the top with “wow” appeal, with blooms upwards of 6” across in absolutely gorgeous shades of pink, red, purple, white, and orange, often with dramatic dark centers. Dig up a section at the edge of the plant and cut off a healthy piece of root, dividing it into 3in (7.5cm) lengths. Poppies are very particular about their roots, so plant as soon as possible after being divided.

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If you try to divide them without having a large root clump, you could damage the roots and kill both plants (or the one plant made two).
Oriental poppies do best when divided and transplanted in the fall. Plant the new divisions in deep holes that are at least 15 feet apart from each other. Take a good sized clump of soil with them to disturb the fleshy roots as little as possible. Dividing Oriental Poppies Posted on August 5, 2009 by Michael Weishan August 15, 2009 This spring the clump of ‘Victoria Louise’ oriental poppies in the long border sent up at least 50 blooms. Discover 10 oriental poppies to grow . They make perfect candidates for this propagation method as it exploits the plant’s propensity to reproduce itself from every scrap of … How to Split, Thin and Care for a Poppy Flower. Best ways to grow non-edibles. Plant the new divisions in deep holes that are at least 15 feet apart from each other.

However, if you are waiting to claim the spot where they are now, I'd take a chance on moving them right away.
This is the traditional way. Share and learn with the UK's largest growing community.

Prepare a sunny, well-drained planting spot for the divisions ahead of time. Divide Oriental poppies in late August or September when the poppies begin to regrow. Oriental poppies generally don’t respond well to division and transplantation, but that doesn’t mean that it’s an impossible feat to perform..

It's a good idea to plant Oriental poppies in the back of the flower bed so other plants will hide the foliage of the Oriental poppy when it begins … Dividing poppies should only be done if the clump of poppies or poppy roots is large. Oriental poppies are a stunning addition to a border and are easy to propagate by taking root cuttings.

Poet John Keats described joy as having his hand ever at his lips, bidding adieu. Be sure to water them well the night before and have their new place ready.