要备份和恢复EncryptedSharedPreferences，您可以按照以下步骤进行操作：

1. 首先，确保您的应用程序具有读取和写入外部存储的权限。您可以在应用程序的清单文件（AndroidManifest.xml）中添加以下权限：

2. 创建一个辅助类来执行备份和恢复操作。可以使用以下代码示例：

import android.content.Context;
import android.content.SharedPreferences;
import android.preference.PreferenceManager;
import android.util.Log;

import java.io.File;
import java.io.FileInputStream;
import java.io.FileOutputStream;
import java.io.IOException;

public class SharedPreferencesBackup {

    private static final String TAG = "SharedPreferencesBackup";

    // 备份文件的名称
    private static final String BACKUP_FILE_NAME = "shared_prefs_backup.xml";

    // 备份EncryptedSharedPreferences
    public static void backup(Context context) {
        try {
            // 获取EncryptedSharedPreferences文件路径
            File sharedPreferencesFile = new File(context.getApplicationInfo().dataDir + "/shared_prefs", "your_encrypted_preferences.xml");

            // 创建备份文件
            File backupFile = new File(context.getExternalFilesDir(null), BACKUP_FILE_NAME);

            // 复制EncryptedSharedPreferences文件到备份文件
            FileInputStream inStream = new FileInputStream(sharedPreferencesFile);
            FileOutputStream outStream = new FileOutputStream(backupFile);
            byte[] buffer = new byte[1024];
            int length;
            while ((length = inStream.read(buffer)) > 0) {
                outStream.write(buffer, 0, length);
            }
            inStream.close();
            outStream.close();
            
            Log.d(TAG, "EncryptedSharedPreferences backup completed");
        } catch (IOException e) {
            e.printStackTrace();
            Log.e(TAG, "EncryptedSharedPreferences backup failed");
        }
    }

    // 恢复EncryptedSharedPreferences
    public static void restore(Context context) {
        try {
            // 获取备份文件路径
            File backupFile = new File(context.getExternalFilesDir(null), BACKUP_FILE_NAME);

            // 获取EncryptedSharedPreferences文件路径
            File sharedPreferencesFile = new File(context.getApplicationInfo().dataDir + "/shared_prefs", "your_encrypted_preferences.xml");

            // 复制备份文件到EncryptedSharedPreferences文件
            FileInputStream inStream = new FileInputStream(backupFile);
            FileOutputStream outStream = new FileOutputStream(sharedPreferencesFile);
            byte[] buffer = new byte[1024];
            int length;
            while ((length = inStream.read(buffer)) > 0) {
                outStream.write(buffer, 0, length);
            }
            inStream.close();
            outStream.close();
            
            Log.d(TAG, "EncryptedSharedPreferences restore completed");
            
            // 重新加载EncryptedSharedPreferences
            SharedPreferences preferences = PreferenceManager.getDefaultSharedPreferences(context);
            preferences.reload();
        } catch (IOException e) {
            e.printStackTrace();
            Log.e(TAG, "EncryptedSharedPreferences restore failed");
        }
    }
}

3. 在需要备份和恢复的位置调用SharedPreferencesBackup.backup(context)和SharedPreferencesBackup.restore(context)方法，将context替换为您的上下文对象。

// 备份EncryptedSharedPreferences
SharedPreferencesBackup.backup(context);

// 恢复EncryptedSharedPreferences
SharedPreferencesBackup.restore(context);

请确保在备份和恢复过程中处理可能出现的异常，并根据需要进行适当的错误处理。