Leland Rechis, Mobile UI designer at Twitter, in the blog post called this new capability 'Fast Follow' and stated that even without a Twitter account anyone can receive Tweets on their phone (available only for US users). However, sending tweets via SMS requires an account, and Fast Followers are not indicated on the accounts they follow.
To set-up SMS Tweets alert from your computer requires going to the Twitter users account you wish to follow and click on the phone icon that is displayed on the hovercard.
Also, its just as easy to set-up via your mobile device, simply send: on (username) or off (username) to 40404 in the United States. Turn SMS alert on or off by adding on or off to the username and text to 40404.
For activation codes in other countries, checkout embedded link on list of numbers for each country. Also additional information on Twitter mobile developments can be found on @twittermobile.
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