Move a cardoon

When we moved here, there was an enormous cardoon in a partially shaded border, although it had its head in the sun. The border became shadier and the old cardoon disappeared. It had seeded a new plant into another, sunnier border, where it  is unfortunately unsuitable as it gets battered by strong winds and also looks out of place. Can I move it? If so when? And could it go back to where the parent  plant was, if I keep that border clearer to allow in more sun? We do struggle for shelter from the wind in this garden, so options are limited.