Why does Nepos use the accusative here?

My son was assigned an excerpt from the Vitae of Nepos, Lysander 4, and hit a snag at the end of this sentence:

nam cum Lysander praefectus classis in bello multa crudeliter avareque fecisset deque iis rebus suspicaretur ad cives suos esse perlatum, petiit a Pharnabazo ut ad ephoros sibi testimonium daret, quanta sanctitate bellum gessisset sociosque tractasset, deque ea re accurate scriberet: magnam enim eius auctoritatem in ea re futuram.

One can sort of intuit that the bold part at the end means something like “for his authority would be great in this matter”, and that more or less matches a public-domain translation that I found online.

But I can’t figure out, in the grammatical context, why magnam … auctoritatem … futuram is accusative. As Draconis has pointed out in the comments, this feels like an indirect statement with an implied esse rounding out futuram, but it seems like the text should include one more verb that introduces the indirect statement; something like “he thought” or the like.

Is there maybe a classical idiom in play here that I’m unaware of? (I’m more familiar with medieval Latin)