First that engine listed for the F510. Actual model number/spec is PA420A-A
S01. The F525 should had the PA540A unitized engine. The F510 came with a 38" deck and the F525 came either a 46" or 48" deck. The one in my shop has the 48" deck.
You will have determine which of the wiring schematics below you will needs since no serial is posted.
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The closest IPL I find for the engine your posted is the Kawasaki PA420A-AS02.which most parts are the same. ANd note many of this unitized engine/power train unit are NLA.