Save on GDoc any SMS from contact
If
New SMS received from phone number
This Trigger fires every time you receive an SMS on your Android device from a phone number you specify.
Then
Append to a document
This action will append to a Google document as determined by the file name and folder path you specify. Once a file’s size reaches 2MB a new file will be created.
Discover more time saving integrations for Android SMS and Google Docs