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Need an app that can forward SMS to another phone or desktop/cloud
(discuss.tchncs.de)
F-Droid is an installable catalogue of FOSS (Free and Open Source Software) applications for the Android platform. The client makes it easy to browse, install, and keep track of updates on your device.
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I like the SMS gate app from f-droid suggested.
A different approach to read SMS from other devices, for example your PC, would be using kdeconnect. It's supposed to allow you to read current messages, receive messages, and reply to messages, even send messages I believe. So perhaps an option, though not a syncing tool to keep SMS messages somewhere else, and I can't tell about the encryption involved...