How to override plugin code

I am using Cyclone Slider 2 plugin for slideshow on my website. The plugin gives you an option in admin to add link where the slide should go to, however the link works only on image, not on the caption. So I found the php file with the markup and I added
<a class="cycloneslider-caption-more" href="<?php echo $slide['link'];?>">
around the caption code. It works fine, but the problem is that if client updates the plugin later on, that change would be gone – how can I prevent this? I read on some previous posts that you can override plugin in functions.php file but I couldn’t find any instructions on how to do this, anyone ?
(It would be nice if there is simple option like in Joomla to override plugins – you just copy file to your template folder)