When I make the register and I introduce all fields included Custom Fields, It not save this Custom fields. Only save if I Save this backend plugin configuration or create in backend user plugin users.

Are you using Custom fields with the RainLab Users plugin?
Do you want to keep the value of the custom fields in the front end?

You need to store the form data in the handler.

example

function onSave()
    {

        $data = post();

        $rules = [
            'name' => 'required',
            'email' => 'required|email',
            'password' => 'confirmed|min:8',
        ];

        $validation = Validator::make($data, $rules);

        if ($validation->fails()) {
            throw new ValidationException($validation);
        }

        $id = input('id');

        $user = UserModel::where('id', $id)->first();

        $user->fill($data);

        $user->setField('usercustomfields', [[
                "first" => input('first'),
                "second" => input('second'),
                "photo" => input('notchangephoto'),

         ]]);

        $user->save();

        Flash::success('Successfully saved!');

        if (array_key_exists('password', $data) && strlen($data['password'])) {

            Auth::login($user->reload(), true);

        }

    }

Yes Vladimir I use user plugin. My code is more complex, the problem is that not create de Custom fields when save data.

function onSave() {

    $data = Input::all();

    $rules = [
        'name' => 'required',
        'email' => 'required|email',
        'password' => 'confirmed|min:8',
        'nickname' => 'required',
        'types' => 'required',
    ];

    $validation = Validator::make($data, $rules, Lang::get('ledel.profile::validation'));

    if ( $validation->fails() ) {
        throw new ValidationException($validation);
    }

    $user = Auth::getUser();
    $id = $user->id;

    $user = UserModel::where('id', $id)->first();

    $user->fill( $data );

    if ( post('types') ) {
        $types = Type::whereIn('id', post('types'))->get();
        $user->types = $types;
    }

    if ( isset( $data['origins'] ) ) {
        $origins = Origin::whereIn('id', post('origins'))->get();
    } else {
        $origins = Origin::where('id', 1)->get();
    }
    $user->origins = $origins;

    if ( isset( $data['orientations'] ) ) {
        $orientations = Orientation::whereIn('id', post('orientations'))->get();
    } else {
        $orientations = Orientation::where('id', 1)->get();
    }
    $user->orientations = $orientations;

    if ( isset( $data['genders'] ) ) {
        $genders = Gender::whereIn('id', post('genders'))->get();
    } else {
        $genders = Gender::where('id', 1)->get();
    }
    $user->genders = $genders;

    if ( isset( $data['languages'] ) ) {
        $languages = Language::whereIn('id', post('languages'))->get();
    } else {
        $languages = Language::where('id', 1)->get();
    }
    $user->languages = $languages;

    if ( isset( $data['sports'] ) ) {
        $sports = Sport::whereIn('id', post('sports'))->get();
    } else {
        $sports = Sport::where('id', 1)->get();
    }
    $user->sports = $sports;

    if ( isset( $data['hobbies'] ) ) {
        $hobbies = Hobby::whereIn('id', post('hobbies'))->get();
    } else {
        $hobbies = Hobby::where('id', 1)->get();
    }
    $user->hobbies = $hobbies;

    $user->birthday = input('birthday');

    $user->smoke = input('smoke');

    if ( input('nickname') && input('birthday') && input('name') && input('surname') && input('description') && input('country_id') ) {
        $user->show = 1;
    }

    $filename1 = input('notchangephoto');
    $filename2 = input('notchangephotoone');
    $filename3 = input('notchangephototwo');

    if (Request::hasFile('photo')) {
        $mediafilename = '/media/avatars/' . $user->id . '/' . 'avatar_' . Request::file('photo')->getClientOriginalName();
        $filename1 = 'avatars/' . $user->id . '/' . 'avatar_' . Request::file('photo')->getClientOriginalName();

        Storage::put($mediafilename, file_get_contents(Request::file('photo')->getRealPath()));
    } else {
        $filename1 = "";
    }

    if (Request::hasFile('photoone')) {
        $mediafilename = '/media/avatars/' . $user->id . '/' . 'photoone_' . Request::file('photoone')->getClientOriginalName();
        $filename2 = 'avatars/' . $user->id . '/' . 'photoone_' . Request::file('photoone')->getClientOriginalName();

        Storage::put($mediafilename, file_get_contents(Request::file('photoone')->getRealPath()));
    } else {
        $filename2 = "";
    }

    if (Request::hasFile('phototwo')) {

        $mediafilename = '/media/avatars/' . $user->id . '/' . 'phototwo_' . Request::file('phototwo')->getClientOriginalName();
        $filename3 = 'avatars/' . $user->id . '/' . 'phototwo_' . Request::file('phototwo')->getClientOriginalName();

        Storage::put($mediafilename, file_get_contents(Request::file('phototwo')->getRealPath()));
    } else {
        $filename3 = "";
    }

    $user->setField('images', [[
        "avatar" => $filename1,
        "photoone" => $filename2,
        "phototwo" => $filename3,
    ]]);

    $user->setField('personal', [[
        "nickname" => input('nickname'),
        "description" => input('description'),
        "location" => input('location'),
    ]]);

    $user->save();

    Flash::success('Successfully saved!');

    $this['countries'] = Country::get();
    $this['situations'] = Situation::get();
    $this['complexions'] = Complexion::get();
    $this['eyes'] = Eye::get();
    $this['hairs'] = Hair::get();
    $this['sons'] = Son::get();
    $this['professionals'] = Professional::get();
    $this['rents'] = Rent::get();
    $this['studies'] = Study::get();
    $this['beliefs'] = Belief::get();
    $this['zodiacs'] = Zodiac::get();
    $this['heights'] = Height::get();

    $this['auxCountry'] = $data['country_id'];
    $this['auxTypes'] = $data['types'];
    $this['auxOrigins'] = $origins->toArray(); 
    $this['auxSituation'] = $data['situation_id']; 
    $this['auxGenders'] = $genders->toArray(); 
    $this['auxOrientations'] = $orientations->toArray(); 
    $this['auxComplexion'] = $data['complexion_id']; 
    $this['auxEye'] = $data['eye_id']; 
    $this['auxHair'] = $data['hair_id']; 
    $this['auxSon'] = $data['son_id']; 
    $this['auxProfessional'] = $data['professional_id']; 
    $this['auxStudy'] = $data['study_id']; 
    $this['auxBelief'] = $data['belief_id']; 
    $this['auxLanguages'] = $languages->toArray(); 
    $this['auxSports'] = $sports->toArray(); 
    $this['auxHobbies'] = $hobbies->toArray();
    $this['auxZodiac'] = $data['zodiac_id'];
    $this['auxEmail'] = $data['email']; 
    $this['auxBirthday'] = input('birthday');
    $this['auxHeight'] = input('height_id');
    $this['auxSmoke'] = input('smoke');

    return [
        '#myTypes' => $this->renderPartial('templates/types'),
        '#myOrigins' => $this->renderPartial('templates/origins'),
        '#myOrientations' => $this->renderPartial('templates/orientations'),
        '#myLanguages' => $this->renderPartial('templates/languages'),
        '#mySports' => $this->renderPartial('templates/sports'),
        '#myHobbies' => $this->renderPartial('templates/hobbies'),
        '#myGenders' => $this->renderPartial('templates/genders'),
        '#myBirthday' => $this->renderPartial('templates/birthday'),
    ];    

}

If possible send me backend login details so I can find the reason.
https://octobercms.com/author/Pkurg
or email: pkurg@pkurg.ru

I have updated the plugin to version 2.2.2