We already claim extraterritorial application of our laws to the whole of humanity.
If, for instance, a Columbian drug lord blows up an airplane in an attempt to assassinate the Columbian VP, and happens to kill an American or two in the process ... we can extradite him, try him, and execute him. This exact scenario occurred with Pablo Escobar — who spent the last couple of years of his life doing everything he could to prevent Columbia from legalizing extradition to the US.
There is no jurisdicitonal difference between a foriegn actor killing an American in a foreign country ... and a foreign actor soliciting an American soldier to steal American secrets from a foreign country.
Jurisdiction depends on what he did, and to whom ... not who he is or where he did it. My understanding of the espionage act is that we already have jurisdiction.
SnakeDoc
Already claim and ought to claim are two different things. Other, unfriendly, powers will return the disfavor.