Post filter Month dropdown at front-end like wordpress backend

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wp_get_archives creates its links with the function get_archives_link. this function returns plain HTML, but it has a filter you can hook into.

You can use the get_archives_link filter to manipulate your HTML with some regex.

function my_archives_link($link_html) {
    //TODO: my regex to manipulate the HTML
    return $link_html;
}

add_filter('get_archives_link','my_archives_link')

Further reading