Apple ID has been disable , how to enable and reset password

First, just clearing my doubt, did he try checking the mail in a popular browser or any device? , just a guess, may be due to the browser agent, he might not be able to view the image or link.

Now if this is not working he has another option to use the secret question option. If he doesn't remember that , just ask him to mail apple support with his mail id and username ,and they can help you , they really do too..

If you don't want to try one more time to reset the password, you might need to contact Apple's support to have them reset your account.

It's entirely possible that the account is either locked or someone else is trying to reset the password (or far more likely another device you have stored the old password keeps repeatedly trying to enter that old password and is causing the account to get locked.)

You can try logging into https://appleid.apple.com from a web browser and see if you really have the correct password. Once you're certain the account isn't locked, you can then sign out of all your OS X and iOS devices to ensure that the old password is cleared and not stored incorrectly.

If your account is locked due to too many incorrect attempts - you will need to contact Apple to get things sorted.