Facebook – How to Activate Group Insights

Facebook Help Center says:

Our system automatically deletes groups once they're empty (no members). If you created the group, you can delete the group by removing all members and then yourself. Note that if you were not the first admin and creator of this group, you will not be able to delete the group unless the group creator has left it voluntarily.

My friend left my group. How can I send a second invitation?
Unfortunately, you will not be able to send a second group invitation to the same friend. The person will have to request to join the group again.

That's from Facebook Help, so my best suggestion is to make it open (or even closed, since one can ask to join a closed group) and let this take effect before your friend starts searching it. I could be wrong, but my guess is he could not find/join it because of the fact that the change is not instant.