This is the second half of a 2 part recipe.With both recipes all SMS messages received and sent are recorded in a spreadsheet in Google Drive.
Other half is here: https://ifttt.com/recipes/165475-sms-timeline
This Trigger fires every time you send an SMS on your Android device.
This action will add a single row to the bottom of the first worksheet of a spreadsheet you specify. Note: a new spreadsheet is created after 2000 rows.
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Google Sheets and Android SMS