Check the single phase motor for hp rating: OEM is 7.5hp. What is a bit odd is that right behind the lathe on the wall (first pic of the add) there is a 3 ph panel. Why would they switch to 1ph if they have 3ph? Make it easier to sell?
Generally, installing a 1ph motor into a 3ph circuit is not difficult. Circuit can basically be the same as long as correct size conductors and components (relays, switches, etc) are used. A 3ph relay can be used to control 1ph power - but not the other way around.
From factory, the power distribution box uses the DIN standard components and layout typical of European machines: no loose wires, everything neatly tucked away in wire tracks, everything labelled, etc.
If the panel still looks like that and everything works electrically, I would have confidence that they did a decent 3ph to 1ph conversion.