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Finally find a way to do this easily

The packedproductID  is the ID of the new product and the productID is the ID of the original product, the one you want to take pictures.

function setProductImage($packedProductID, $productID)
{
    $packedProdImgs = getProductImage($packedProductID);
    foreach ($packedProdImgs as $imgs) {
        $image = new Image();
        $image->id_product = $productID;
        $image->position = $imgs['position'];
        if ($imgs['cover'] == 1) {
            $image->cover = true; // or false;
        } else {
            $image->cover = false;
        }
        if ($image->add()) {
            if (!copyImg($productID, $image->id, $imgs['url'], 'products', true)) {
                $image->delete();
            }
        }
    }
}

Aux functions :

function copyImg($id_entity, $id_image = null, $url, $entity = 'products', $regenerate = false)
{
    $tmpfile = tempnam(_PS_TMP_IMG_DIR_, 'ps_import');
    $watermark_types = explode(',', Configuration::get('WATERMARK_TYPES'));

    switch ($entity) {
        default:
        case 'products':
            $image_obj = new Image($id_image);
            $path = $image_obj->getPathForCreation();
            break;
    }

    $url = urldecode(trim($url));
    $parced_url = parse_url($url);

    if (isset($parced_url['path'])) {
        $uri = ltrim($parced_url['path'], '/');
        $parts = explode('/', $uri);
        foreach ($parts as &$part) {
            $part = rawurlencode($part);
        }
        unset($part);
        $parced_url['path'] = '/' . implode('/', $parts);
    }

    if (isset($parced_url['query'])) {
        $query_parts = array();
        parse_str($parced_url['query'], $query_parts);
        $parced_url['query'] = http_build_query($query_parts);
    }

    if (!function_exists('http_build_url')) {
        require_once(_PS_TOOL_DIR_ . 'http_build_url/http_build_url.php');
    }

    $url = http_build_url('', $parced_url);

    $orig_tmpfile = $tmpfile;

    if (Tools::copy($url, $tmpfile)) {
        // Evaluate the memory required to resize the image: if it's too much, you can't resize it.
        if (!ImageManager::checkImageMemoryLimit($tmpfile)) {
            @unlink($tmpfile);
            return false;
        }

        $tgt_width = $tgt_height = 0;
        $src_width = $src_height = 0;
        $error = 0;
        ImageManager::resize($tmpfile, $path . '.jpg', null, null, 'jpg', false, $error, $tgt_width, $tgt_height, 5, $src_width, $src_height);
        $images_types = ImageType::getImagesTypes($entity, true);

        if ($regenerate) {
            $previous_path = null;
            $path_infos = array();
            $path_infos[] = array($tgt_width, $tgt_height, $path . '.jpg');
            foreach ($images_types as $image_type) {
                $tmpfile = get_best_path($image_type['width'], $image_type['height'], $path_infos);

                if (ImageManager::resize($tmpfile, $path . '-' . stripslashes($image_type['name']) . '.jpg', $image_type['width'], $image_type['height'], 'jpg', false, $error, $tgt_width, $tgt_height, 5, $src_width, $src_height)) {
                    // the last image should not be added in the candidate list if it's bigger than the original image
                    if ($tgt_width <= $src_width && $tgt_height <= $src_height) {
                        $path_infos[] = array($tgt_width, $tgt_height, $path . '-' . stripslashes($image_type['name']) . '.jpg');
                    }
                    if ($entity == 'products') {
                        if (is_file(_PS_TMP_IMG_DIR_ . 'product_mini_' . (int) $id_entity . '.jpg')) {
                            unlink(_PS_TMP_IMG_DIR_ . 'product_mini_' . (int) $id_entity . '.jpg');
                        }
                        if (is_file(_PS_TMP_IMG_DIR_ . 'product_mini_' . (int) $id_entity . '_' . (int) Context::getContext()->shop->id . '.jpg')) {
                            unlink(_PS_TMP_IMG_DIR_ . 'product_mini_' . (int) $id_entity . '_' . (int) Context::getContext()->shop->id . '.jpg');
                        }
                    }
                }
                if (in_array($image_type['id_image_type'], $watermark_types)) {
                    Hook::exec('actionWatermark', array('id_image' => $id_image, 'id_product' => $id_entity));
                }
            }
        }
    } else {
        @unlink($orig_tmpfile);
        return false;
    }
    unlink($orig_tmpfile);
    return true;
}

function get_best_path($tgt_width, $tgt_height, $path_infos)
{
    $path_infos = array_reverse($path_infos);
    $path = '';
    foreach ($path_infos as $path_info) {
        list($width, $height, $path) = $path_info;
        if ($width >= $tgt_width && $height >= $tgt_height) {
            return $path;
        }
    }
    return $path;
}

These functions are normally available in AdminImportController