Move Jetpack's Related Posts

custom-functions.php

<?php

// Let's unhook the original filter
function jetpackme_remove_rp() {
	$jprp = Jetpack_RelatedPosts::init();
	$callback = array( $jprp, 'filter_add_target_to_dom' );
	remove_filter( 'the_content', $callback, 40 );
}
add_filter( 'wp', 'jetpackme_remove_rp', 20 );

single.php

<?php 

// Let's add the Related Posts shortcode to our template
do_shortcode( '[jetpack-related-posts]');

Thanks for sharing. Now it works doing:

single.php

echo do_shortcode( '[jetpack-related-posts]');