I want to send text messages to a friend who are in China now on China Mobile via email. I am in US. Does China Mobile supports this and how can I do?

First your friend need to activate GPRS on its China Mobile SIM card.
Next your friend need to activate its 139 email service (it's free but only Chinese version available)
Then you can send email to your friend's mobile email. it looks 1xxxxxxx@139.com and he can directly read your email with its mobile phone.

yes, of course you can do it, most of china mobile support GPRS connection.

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