public class MainActivity extends AppCompatActivity implements View.OnClickListener {

public static final String TAG = "activity_main";

private FirebaseAuth mAuth;
private FirebaseAuth.AuthStateListener mAuthListner;
private TextView email;
private TextView password;
private ProgressBar progressBar;
SharedPreferences mSettings;
public static final String APP_PREFERENCES_USER = "User";
public static final String APP_PREFERENCES = "mysettings";

protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(layout.activity_main);

    mAuth = FirebaseAuth.getInstance();     // get instance of fireBase

    progressBar = (ProgressBar)findViewById(id.progressBar);

    email = (TextView) findViewById(id.email);
    password = (TextView) findViewById(id.password);

    **mSettings = getSharedPreferences(APP_PREFERENCES, Context.MODE_PRIVATE);
    if(mSettings.contains(APP_PREFERENCES_USER)){
        email.setText(mSettings.getString(APP_PREFERENCES_USER, "rea"));
    }**

    mAuthListner = new FirebaseAuth.AuthStateListener() {
        @Override
        public void onAuthStateChanged(@NonNull FirebaseAuth firebaseAuth) {
            FirebaseUser user = firebaseAuth.getCurrentUser();
            if (user != null) {
                Log.d(TAG, "Sign_in" + user.getUid());
            } else {
                Log.d(TAG, "Sign_out");
            }
        }
    };

    findViewById(id.sign_in_Button).setOnClickListener(this);
    findViewById(id.registration_Button).setOnClickListener(this);
}

public void onStart() {
    super.onStart();
    mAuth.addAuthStateListener(mAuthListner);
}

public void onStop() {
    super.onStop();
    if (mAuthListner != null) {
        mAuth.removeAuthStateListener(mAuthListner);
    }
}

@Override
public void onClick(View v) {
         if (v.getId() == id.sign_in_Button) {
             if ((!email.getText().toString().equals(null) && !email.getText().toString().equals(""))
                     || (!password.getText().toString().equals(null)&& !password.getText().toString().equals(""))) {
                 progressBar.setVisibility(View.VISIBLE);
                 mAuth.signInWithEmailAndPassword(email.getText().toString(), password.getText().toString())
                         .addOnCompleteListener(this, new OnCompleteListener<AuthResult>() {
                             @Override
                             public void onComplete(@NonNull Task<AuthResult> task) {
                                 if (task.isSuccessful()) {
                                    **Editor editor = mSettings.edit();
                                     editor.putString(APP_PREFERENCES_USER, email.getText().toString());
                                     mSettings.edit().apply();**
                                     if (email.getText().toString().equals("admin@rea.ru")) {
                                         Intent intent = new Intent(MainActivity.this, admin_Activity.class);
                                         startActivity(intent);
                                         progressBar.setVisibility(View.INVISIBLE);
                                     } else{
                                         Log.d(TAG, "Succesful enter");
                                         Intent intent = new Intent(MainActivity.this, Categories.class);
                                         startActivity(intent);
                                         progressBar.setVisibility(View.INVISIBLE);
                                     }
                                 }
                             }
                         })
                         .addOnFailureListener(new OnFailureListener() {
                             @Override
                             public void onFailure(@NonNull Exception e) {
                                 Toast.makeText(MainActivity.this, e.getMessage(), Toast.LENGTH_SHORT).show();
                             }
                         });
             }else{
                 Toast.makeText(MainActivity.this, "Password or email is empty", Toast.LENGTH_SHORT).show();
             }
         }

        if (v.getId() == id.registration_Button) {
            progressBar.setVisibility(View.VISIBLE);
            Intent intent = new Intent(MainActivity.this, RegistrationActivity.class);
            startActivity(intent);
            progressBar.setVisibility(View.INVISIBLE);
        }
}

Editor editor = mSettings.edit();
 editor.putString(APP_PREFERENCES_USER, email.getText().toString());
 editor.apply();
//вместо mSettings.edit().apply();

mSettings.edit().putString(APP_PREFERENCES_USER, email.getText().toString()).apply();

SharedPreferences mSettings = PreferencesManager.getDefaultSharedPreferences(context);