http://www.creativetechsupport.com/help/it/install/timemachine-inherit.html

Time Machine is Apple’s built-in, set-it-and-forget-it backup system. Time Machine makes hourly snapshots of files and copies them to a backup drive. It keeps older revisions and deleted documents so it can restore them or an entire computer to any point in the past. When the backup drive is full it automatically deletes the oldest backups.

Time Machine works so well it doesn’t always get much attention. But if you need to replace computers or hard drives, you’ll appreciate these advanced techniques that put you in charge of what happens behind the scenes.

Inheriting a backup versus creating a new backup

When you replace a Mac that was previously backed up with Time Machine, you can set it to use the same backup drive as the old Mac as long as there’s enough room for both computers’ backups.

If you used Migration Assistant to set up the new Mac, at the first backup Time Machine may ask if you want to inherit the backup history of the old computer. Note that even if you choose to inherit the backup, Time Machine cannot pick up where it left off and copy only new files. It always copies everything from the new Mac to the backup. Even so, inheriting can have benefits.

Inheriting a backup allows the user to easily restore files from the previous computer’s backup even if they weren’t on the computer when you set up the new Mac. And if the backup drive eventually fills up, Time Machine will seamlessly remove the old Mac’s backups to make room.

Instead, if you create a new backup Time Machine leaves the old backup set intact and starts a new set. That’s great if you plan to continue using both Macs but it’s not convenient if you intend to sell or dispose of the old Mac. You may run out of space and have to remove the old backup set manually. That’s not always easy because, as Time Machine will tell you, “backup items cannot be modified.”

Forcing a Mac to inherit a backup

1. On the new Mac, set Time Machine to use the same backup drive as before. Then immediately turn backups off.
2. Log in as an admin user and open Terminal.
3. Type or copy & paste the following command: sudo tmutil inheritbackup and a space.
4. If the Mac backs up to a local drive, open the backup drive and the Backups.backupdb folder. Drag the folder named after the old computer to the terminal window.
5. If you back up to a network (such as a Time Capsule or server), mount the backup volume and look for the Mac’s backup disk image inside. Do not open it – just drag the disk image to the terminal window.
6. Click the terminal window, hit return and type the admin password.

Replacing a drive and continuing the same backup

When you replace a hard drive in a Mac that was backed up with Time Machine it’s usually considered an entirely new volume. Everything is backed up from scratch. Although the original drive may also show in Time Machine this will undoubtedly take a lot of time and space. In fact, Time Machine may delete a good part of your backup history (maybe all of it) to make room for the new drive. Thankfully, there’s a better way.

Associating a new drive with a Time Machine backup

1. Turn off Time Machine backups – preferably just before you transfer files to the new drive.
2. Use a tool like Carbon Copy Cloner when you replace a drive. This utility makes a clean copy and preserves file ownership & permissions. The less your new drive differs from the original the less Time Machine will have to recopy when you back up.