They can't, which is why you can't easily be extradited from the UK for foreign crimes that aren't also crimes in the UK. Unfortunately for him, the crime he's charged with is also 1:1 a crime in the UK.
But if you look at the case of Christopher Tappin, who was caught in an FBI sting allegedly exporting missile batteries to Iran...
1. The batteries were dual use
2. He never actually did the deal, he was named as the exporter by the guy who did
3. He thought the batteries were going to Holland.
Now there may be more to this than we know, but none of the above is a crime in the UK
