As you saw somebody in action of doing something , the best option would be: I saw him stealing the money .
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CliveHi,
I saw him stealing the money (past tense verb+ing) As already pointed out, this stresses that you saw him 'in the act'.
I saw he steal the money (correct) Incorrect. You need 'him', not 'he'. This stresses you saw the completed act.
I saw he stole the money