In android is there any way to preserve SharedPreferences after an uninstall

I'm pretty sure SharedPreferences is always deleted along with the app. In my opinion, the best way to do this would be to write a hidden file (something like ".nameOfFile") onto the SD Card or internal memory and have that contain the preferences as well.

You should use SharedPreferences though, it's the Android standard for preference management. You could make it so that the first time your app loads, it checks the SDCard for a hidden file that would have been created last time they opened it. If the file exists, then read in those inputs and store them in the SharedPreferences, if it doesn't, then either the user deleted it or the user has never installed your app before.

This is just one way to do it, and it might not be the most efficient, but I hope it helps!

Since Android 6.0 it has been possible to use:

<application
        android:allowBackup="true">

By setting it to true your data (sharedprefs and others) will be saved on Google cloud and restored next time the app is installed. You can read more about it here. It should be noted that the default settings is true since 6.0.

One way to do this would be to store the user data on a server. Then when the user re-installs the app or installs the app on another device, they can "sync" their user data. That would just be a small HTTP download of the data, likely stored in JSON, which you would then parse and write into the SharedPreferences.

If you don't want to maintain your own server, you could use a cloud service like Dropbox. This is how the app 1Password Reader works.

You should add a BackupAgentHelper to your app. Together with the SharedPreferenceBackupHelper, it backups the SharedPreferences to the cloud (if the device supports it). When the app is reinstalled the data is restored.

See:

BackupAgentHelper

SharedPreferenceHelper (contains all the code you need to implement it)

general Backup guide