Change the publish date of a distributed post to the source timestamp

distributor-post-date.php

<?php

namespace BigWing\Integrations\Distributor;

/**
 * Set the date on distributed posts to the source date.
 *
 * @param array    $post_args The post data to insert into the receiving site.
 * @param \WP_Post $post      The source post object.
 *
 * @return array The modified post data.
 */
function set_date_on_push( array $post_args, \WP_Post $post ): array {
	$post_args['post_date']         = $post->post_date;
	$post_args['post_date_gmt']     = $post->post_date_gmt;
	$post_args['post_modified']     = $post->post_modified;
	$post_args['post_modified_gmt'] = $post->post_modified_gmt;

	// Don't overwrite pub date during updates.
	if ( isset( $post_args['ID'] ) ) {
		$post_args['post_date']     = date( 'Y-m-d H:i:s', get_post_time( 'U', false, (int) $post_args['ID'] ) );
		$post_args['post_date_gmt'] = date( 'Y-m-d H:i:s', get_post_time( 'U', true, (int) $post_args['ID'] ) );
	}

	return $post_args;
}

add_filter( 'dt_push_post_args', __NAMESPACE__ . '\\set_date_on_push', 10, 2 );