You can just save a string representation of your URI.
SharedPreferences settings = getSharedPreferences(PREFS_NAME, 0);
SharedPreferences.Editor editor = settings.edit();
editor.putString("imageURI", imageUri.toString()); <-- toString()
Then use the Uri parse method to retrieve it.
SharedPreferences settings = getSharedPreferences(PREFS_NAME, 0);
String imageUriString = settings.getString("imageURI", null);
Uri imageUri = Uri.parse(imageUriString); <-- parse
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