SMS Gate appSMS Gate is System tool that is open source under the GPL-3.0-only license. You should be able to control all data produced by your phone and be able to
collect it all into one place (cloud / p2p or local).
SMS Gate app backups all your SMS from Android/INCOMING folder to the
IMAP/INBOX folder of Gmail or your provider of choice (you can setup one in
Settings). Once uploaded to an IMAP server you can even reply to the SMS
using standard reply e-mail mechanics.
Saving to a local folder allows you to backup it using an app like