How can I set my Galaxy S3 to vibrate when locking the screen? My partner and I have identical Galaxy S3's.

However when my phone locks it briefly vibrates, when partner's locks it does not. What setting have I changed that makes this happen on mine and not on his?
Go to the main Android SETTINGS > SECURITY > SCREEN LOCK

Now see if there are any differences between the options as configured on your device and the other one.

Try ticking the option VIBRATE ON TAP to activate haptic feedback.