Progressify

Overview
Progressify is a plugin which allows you to convert your website into PWA (Progressive Web App), including sending push notifications to your users.
Special integration is required to send messages notifications from Better Messages to your users, which is now included in Better Messages plugin.
Installation
- Get Progressify from official website and install following standard WordPress installation process
- Configure Progressify plugin and enable push notifications in Progressify settings
Better Messages will automatically detect Progressify plugin and enable push notifications integration, that will be displayed in Better Messages -> Settings -> Notifications.

Bottom menu overlap fix
If you are using Progressify's bottom navigation menu, it may overlap the Better Messages reply area on mobile devices. Add the following CSS to fix this:
.bp-messages-chat-wrap.bp-messages-mobile,
.bp-messages-single-thread-wrap.bp-messages-mobile,
.bp-messages-wrap-group.bp-messages-mobile,
.bp-messages-wrap-main.bp-messages-mobile {
bottom: 58px !important;
}
You can add this CSS via WP Admin → Appearance → Customize → Additional CSS, or use the better_messages_css_customizations filter.