I've been using
SMS Backup+ on my Android 'phone for some time, which recently proved invaluable when I accidently (still don't know how it happened!) deleted all my sms text messages.
After restoring the messages, I looked at the backup program again and realised I could backup to my FastMail account, instead of to my 'phones default Gmail account.
So I changed the settings within the program, and I now have a folder in my FastMail account with all my text messages.
The beauty of that is, when I backup my FastMail e-mails (using
MailStore Home), I get not only backups of my e-mails but also another backup of my sms text messages.
Check out this link I found for additional info:
https://randomstuffintech.wordpress....with-fastmail/