Yes, there IS a way to search a Facebook group! Watch this video to find out how.
Keep in mind, Facebook’s search algorithm is better than it used to be, but still not comprehensive. I often go looking for a post I know exists in the group, yet the search results fail to turn it up.
If you’re looking to search elsewhere on Facebook, this post by Make Use Of offers 5 Tools To Help You Find Anything In Your Facebook Timeline.