Problem finding rented movie in iTunes

Look under Purchases.

If you actually downloaded the rental on your phone, you cannot transfer it to any other device or computer. That's why it doesn't show, & why you won't be able to view it on your computer.

If you download a rented purchase on any iOS device or Apple TV, it is not transferable to any other device or computer - as mentioned here:

http://support.apple.com/kb/HT1657

This is why I only ever rent movies on iTunes through my Mac, or if I'm watching immediately through Apple TV.

...right - I forgot to add, "on your phone"...

gritzildino wrote:

So I guess it only works from Mac to iPhone and not the other way around...?

Correct.

Not a secret, though, and not much guesswork, either. It's written e.g. here:

Can I play my rental on more than one device?

• If you download a rented movie on your computer: You can transfer it to a device such as your Apple TV (1st generation), iPhone, iPad, or iPod if it’s a standard-definition film (movies in HD can only be watched on your computer, iPad, iPhone 4 or later, iPod touch (4th generation or later), or Apple TV). Once you move the movie from your computer to a device, the movie will disappear from your computer's iTunes library. You can move the movie between devices as many times as you wish during the rental period, but the movie can only exist on one device at a time.
• If you download a rented movie on your iPhone 4 or later, iPad, iPod touch (4th generation or later), or Apple TV: It is not transferable to any other device or computer.