You can take a look at SymmetricDS , I have not used it myself, but I am considering it.
It currently allows SQLite DB on Android to sync with the mongoDB band, but currently not in the other direction. Apparently, you could create the necessary synchronization data in an intermediate synchronization database so that it returns to your SQLite database.
The pipeline also has a version of iOS.
It has a GPL, so you will have to pay (if your application is not open source) if you use it commercially.
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