just look at the vin# on the back of the jetski. the first three letters will probably be kaw (kawasaki) you already said it was a js440 and the last two numbers should be the year. That should cover make, model, and year.
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-1990 X-2 - the weird one
-1987 JS550 - bone stock and staying that way for now
-1984 JS550 - restored, 440 pump, Skat Trak, primer, thumb throttle