To copy a story map first, you need to start by creating a new one:
Select Story maps on the left side panel, then select Add a new story map
Select Create by copy
In the Select a story map to copy dropdown select the map you'd like to copy from, then select Continue.
Add a new name for your story map. You can also add a description and move it to a collection. Select Continue.
On the next screen you can set the visibility and invite or add collaborators, then select Finish.