So I take it Danish doesn't split verbs? (Han sætter fort...)
Not this one at least, and especially not compared to German. In fact, no, I don't think we do that at all!
... or compared to Dutch, voortzetten, voortdoen; hij/zij zet voort, doet voort
In German some prefixes are separated and some are not. In addition some verbs can be separated, but don't have to, and it changes the meaning of the verb as well as the intonation.
What does this mean? That he continues doing whatever he was doing, as in "he keeps at it"? Or that he continues something at his workplace? Or something else?
What's wrong with "han forsætter på sit arbejde"?