Will I have to create 2 different instances of the QSortFilterProxyModel or there is some other way around?

My Code

main.cpp

int main(int argc, char *argv[])
{

    // Application basic initialization
    QCoreApplication::setAttribute(Qt::AA_EnableHighDpiScaling);

    QGuiApplication app(argc, argv);
    QQmlApplicationEngine engine;

    QtWebEngine::initialize();
    QQuickStyle::setStyle("Default");

    FilterModel filterModel;
    FilterList filterList;

    // Set contexts for QML
    engine.rootContext()->setContextProperty("filterModel",&filterModel);
    engine.rootContext()->setContextProperty("filterList",&filterList);


    engine.load(QUrl(QStringLiteral("qrc:/main.qml")));
    if (engine.rootObjects().isEmpty())
        return -1;

    return app.exec();
}

filterlist.cpp

#include "filterlist.h"

FilterList::FilterList(QObject *parent) : QSortFilterProxyModel(parent)
{
    setSourceModel(&m_filterListModel);
}

void FilterList::searchByCategory(QString filterSubCategory)
{

    setFilterRole(m_filterListModel.FilterListCategoryRole);
    this->setFilterCaseSensitivity(Qt::CaseInsensitive);
    this->setFilterFixedString(filterSubCategory);
}

mypage.qml

import QtQuick 2.15
import QtQuick.Controls 2.15
import QtQuick.Layouts 1.3

Page {

    id : somepageid

    Column{
        Button{
            id: btn1
            text: "btn a"
            onClicked: {
                filterList.searchByCategory("category a")
            }
        }

        Button{
            id: btn2
            text: "btn b"
            onClicked: {
                filterList.searchByCategory("category b")
            }
        }
    }

    ListView{
        id: lv1
        model: filterList
        height: 100
        delegate: Row{
            Text{
                text: name
            }
        }
    }

    ListView{
        id: lv2
        anchors.top: lv1.bottom
        model: filterList
        height: 100
        delegate: Row{
            Text{
                text: name
            }
        }
    }

}