[MunchkinMan]

Stealing an Item doesn't somehow change whether Cheat! can be used on it or not. Also, the wording of Cheat! is such that you can play it on any Item you have in play at any time, even if you could already use the Item. Granted, that's not entirely important to the question at hand, but at the same time it does speak to the fact that you can play Cheat! on an Item you can use without Cheat!, if you want to.

So, if you put an Item Enhancer that has a requirement/restriction on an Item, then that Item will have the requirement/restriction. Cheat! will get around that requirement/restriction, since that is its on-the-card defined purpose: It's designed to let you use (and in some cases, like Big Items, carry as well) an Item you normally couldn't, for whatever reason. As I said above, stealing the Item doesn't change its ability to have Cheat! played on it, nor does playing the Item normally.

As an extra, I'll point out that Cheat! does not ever stay with what it is played on when that Item is lost or changes ownership. I.e., a Thief can't steal an Item with Cheat! on it and expect to get the Cheat! card, too.