Drag’n’drop the Event from the Events tab of the Edit Person (or Edit Family) dialog to the Clipboard. (Open the Clipboard from the Edit menu or the toolbar icon.)
open the Edit Person (or Edit Family) dialog for the next participant
Drag’n’drop the Event from the Clipboard to the Events tab of the Edit dialog for the Participant
Change the Role from Unknown to Primary for a person Event, or Family for a family Event.
I tend to sort the Select Event list by “Last Change”. And now the Recent Items addon (from the Isotammi curated collection) eliminates the need to change the sort order.
But if it is not a recently modified Event, then using the ID is a good approach… but still, the clipboard is much easier.
I find that if you open the person with the event and open the person that you want the event to have. Make sure they can both be seen on the screen and drag and drop from the first person to the 2nd person.