It is a wild Pokemon, so no, it does not belong to a trainer. You can't catch other trainer's Pokemon.
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Theres a trainer on route 216 that has one
You can see Sudowoodo in these locations: Route 209 - PKMN Breeder (Male) Albert (VS Seeker Rematch, 2nd change) Route 216 - Ace Trainer (Female) Maria Route 221 - Wild (25% chance)
thers one on route 210 a guy dressed in black and cap
You can breed sudowoodo with another sudowoodo or a ditto. To get another sudowoodo, you will need to trade for one. You can also breed a ditto with a sudowoodo to get another sudowoodo. Make sure you ask the daycare to see if your ditto gets along with the sudowoodo.
Sudowoodo was created in 1999.