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If you can set the customer up with a Mobile number and a provider . You should be able to do it… Ibelive they all have a Email amdress. Just need to send only 140 char
Verizon is firstname.lastname@example.org
Att is email@example.com
But someone needs to add to Customer and the Emails that are sent needs a secound one with just basic information.. ie Order XXXXX Being sent. or Vendor Order XXXXX placed for $34.99 3 items etc