Xbox purchases do not download to console

Hello,

If you purchased the game on your Xbox 360 console and you're not seeing it in the downloadable queue then please do the following:

Go to your Xbox 360 Dashboard > Settings > Account > Download History. If you've purchased it on the console using this gamertag then you should be able to initiate the re-download from there.

Content is licensed to both the gamertag that purchases it as well as the console that it is initially downloaded to. If you've downloaded it to a second console or a replacement console, you may need to do a License Transfer. Without a license transfer,
you will need to be signed into your Xbox Live account in order to access the content.

support.xbox.com/.../download-content

The way Xbox licences work is that the account (Gamertag) that the item was purchased on can be downloaded and played on any Xbox. Also, the first console that it was purchased/downloaded on will be able to be played by any account on that console. the licences
can be transferred (all licences on an account) to another console once a year, for more details on that click

here. In the future if you download the game with your sisters account, do it on your console first then she is free to play it on her Gamertag and you are free to play it on your console.

In order to share the downloaded games, he would have had to sign in to your console as himself first, purchase and download the game on your console. Then go back to his console and download it again.

For most game downloads, the FIRST console you download to, usually lets any profile play the game.

For any console its installed on after the first one, usually the profile that purchased the game will be the ONLY one that can use it.

That's how I do it at home. I download any purchases to the "family" xbox first, then I re-download it on mine afterwards.

You can redownload anything previously downloaded by accessing the download history.

As for achievements not appearing the sam on different consoles, are you not playing while connected to Xbox LIVE on both consoles? So long as you play online and download your profile to the console you are playing on, the achievements will be in sync.
If you play offline on one or both consoles, only one version can be synced to Xbox LIVE and you could wind up needing to achieve those over again.

Info on download history from the Xbox.com website:

Download History

Where can I see items I have purchased?

All items you have purchased from Xbox LIVE Marketplace (including free items and items you purchased using your console) will appear in your Download History. Your purchases are grouped under three categories: Games, Game Demos, and Avatars.

How do I download items I previously purchased from the web?

Go to your Download History and select the Add to Queue button next to the item you want to download again. You can also locate items you own in Xbox LIVE Marketplace and click the Download to Xbox 360 button to add the item to your Download Queue.

How do I return an item purchased from Xbox LIVE Marketplace on the Web?

All items purchased or rented from Xbox LIVE Marketplace, using the Web or your Xbox 360 console, are non-refundable.