American Satirist C.J. Hopkins Sentenced in German Speech Case

Context?

He lives in Germany as a permanent resident. So he can either appeal, pay the fine, or move back to the US (plane tickets alone would cost more than the fine, let alone the cost and disruption of moving a family).

If he lived in the US, he could likely just ignore the ruling. This would clearly be 1A protected speech in the US, so even if Germany pursued it, they would be politely told to screw off. It would probably be a bad idea to return to Germany though.

There's no need to appeal yet. With "punishment order" they probably refer to a german "Strafbefehl" which isn't a full sentence but a simplified system to avoid trials which only requires a bit more than probable cause.

They can now object to it, then there will be a full trial. If they loose there, then they can appeal.

May I point out a slippery slope is that sort of argumentation? American people have some basic rights protected by constitution. If these can be circumvented by shipping their trials to another country, then what's the point?