1939-1945 Star with "BATTLE OF BRITAIN" clasp!

Hello Everyone! I have this 1939-1945 Star with the clasp "Battle of Britain" (https://www.medalbook.com/europe/united-kingdom/medals-decorations/campaign-medals/1939-45-star/1939-45-star-1) … I've heard this is a very rare and desired WW2 clasp for aviation or medal collectors. However, I'm not sure if this is genuine , and if it is genuine how much could it cost?

Here is an interesting site I found: https://www.lancaster.ac.uk/staff/hartleyi/bobclasp.htm

I'm certainly no expert, so hopefully this helps.