Yep you've got it, just to stop the brolly from unravelling , it originally had a bit of velcro to keep it together , you could as you say adapt it with a strap for a shoulder carry but i just wanted something simple that i can throw the strap in my pocket when it's raining as it seems to be every day here in the UK at the moment.
The Brolly is one of those Telescopic type so it's in a closed position in the photo .