I found a solution here:
https://www.ads-software.com/support/topic/270651
$pos=strpos($post->post_content, '<!--more-->');
I have a graphic button that I want to show at a special place only if there is a more tag, and my solution looks like this:
<?php if ($pos=strpos($post->post_content, '<!--more-->')): ?>
<a href="<?php the_permalink() ?>#more-<?php the_id() ?>" class="button"><span><span>L?s hela</span></span></a>
<?php else : ?>
<?php endif; ?>