Construction of to cheat
Solution 1:
You can certainly use the verb to cheat in this context, but you want to avoid the phrasal verb to cheat on [a person], which specifically implies (generally sexual) infidelity within a romantic relationship.
The structure you're probably looking for is X cheated Y out of [his money].
I'm not sure what it would mean to cheat someone of their feelings. If you're confused about how to continue the sentence after the verb, you could always say something like: X cheated Y, causing him to lose a good deal of money.
Solution 2:
In this context a more common construction would be that, "Mr X cheated Mr Y out of some money"
"Cheat on," is more often used in phrases such as, "Mr X cheated on his wife with Mrs Y"
Solution 3:
The other answers are correct. I wish to expand upon them. You cheat on a test, your taxes, your wife, and your diet. You cheat at cards, baseball, and chess. You cheat someone out of money. Basically, usually, you cheat on an object or thing, you cheat at an action or activity, and you cheat a person. Only time you cheat on a person is when it's a relationship fidelity issue.
There are also a lot of interesting synonyms for cheat that usually deal specifically with cheating someone out of money with varying degrees of underhandedness implied. Swindled, hoodwinked, bilked, fleeced, finagled, stiffed, scammed, conned, hornswoggled, bamboozled, etc.
For instance, something like "stiffed" would be used in the case of someone pulling up to a gas station and filling their tank and driving off without paying, or someone borrowing $20 and never paying it back, or if you agree to go halves on dinner and the other guy "forgot" his wallet.