This is routine. Country "A" hands down a sentence, Country "B" agrees to allow the prisoner to serve his time for _that_ sentence, not some other sentence that some other country might impose.
What's different is that things like compassionate release (etc) are determined by the "imprisoning" country.
And although it's unpopular to think it, being tried for a crime potentially related to issues of free speech and a free press is probably far better in the USA (where we have a frickin' Amendment on the subject) rather than in the UK or Australia, where they don't.