Are you sure the axle itself uses that engine oil Ken? It would be fairly unusual. The hydro unit normally uses light oil, but the axle unit usually uses heavy oil, and the two are kept separate - which they have to be anyway, because the axle unit usually accumulates a lot of fine particles of metal, and these would have a disastrous effect on the hydraulic pump and actuator.

I'm not saying it's impossible that the axle uses light oil, but because it would be quite unusual, I suggest you check carefully, and find out what the hydro uses, and what the axle unit uses. If they turn out to be the same stuff, you win the bet. If they don't, losing the bet is better than wearing out your axle unit with the wrong oil.