Well, no real surprise. There is now a black market in forged vaccination certificates in the fatherland, at the end of the day this is going to be everywhere as people with no vaccination are excluded from events or travel. Unfortunately to do such exclusion is tantermount to facism.
I’m not sure about over there. But over here, I’m sure they can check the validity of your vaccine via your NHS number if required. My vaccine, whilst done at work, was still registered with the NHS by the provider.