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Can I and if yes, how do I send text from my PC to any mobile phone?
Typically there's an email address that you can send to.
This is usually something similar to ##########@provider.com - Example, if cell phone number "1234567890" was provided by Verizon Wireless, you would send the message to "email@example.com"
I found this link that seems to be a great reference for the domains of the different providers.
You could also use any one of several messenger services that allow it (Google Chat or AIM, for example).