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This probably depends on your particular dongle model. Back in 3G era, some carriers offered USB modems with SMS locked out in the firmware, but you could flash a firmware from a different operator (also install their variant of software, the only difference being the added SMS tab and a different skin) and then you can text and even use USSD! (No calls, though.)

https://messages.google.com/web/ is one way I'm aware of, I'm sure there's others depending on the messages app used.

It seems those modems run Android 4.x with the stock messaging app: https://github.com/u0d7i/uz801#screenshots

But I guess you can install a custom messaging app that would sync the messages? (If there’s one that still supports such an old version of Android)

yeah my vendor's dongle has this specific feature. A light also turns ON on the modem when SMS is received.