Okay he can absolutely infodump to them about the Pelopennesian War. So! A lot of the interesting bits are actually in the lead up, you need to know a bit about how ancient Greek city states worked. And specifically a bit about Athens. It's really important to understanding the Pelopennesian War that Athens was kind of all-in on their navy and Sparta was much more effective on land. Also here, have some information about how Greek Hoplites fought and the tradeoffs between depth and breadth. Okay he's being sidetracked he'll get back to the actual war things.
The entire time he's explaining things he's animated. He's careful not to brush against Hailey or get anywhere close, though. His face comes alive, he gestures expansively with his hands, at one point he grabs a bit of paper to draw the shape of the Long Walls of Athens. Athens wasn't directly on the coast because you didn't want your city to be easy to raid by sea, usually Greek cities were founded on hills near but not directly on the ocean. They couldn't win on land so they just made a set of absurdly long walls to connect their city to the harbour. Behold the longness of the walls!
He can give them a narrative of the war! It's not a polished one since he hasn't practiced explaining the Pelopennesian War to people but he can do a pretty okay job!