iOS Question imqtt in background

Technically it is possible but your app will not be approved by Apple. You need to use push notifications instead. Once the notification is received you can connect with MQTT.

Thanks, i need that users of b4a send/receive message with users of b4i , is better to change in b4a mqtt to push notification and developper b4a and b4i with the same protocol push notification?

You should use both Firebase push notifications and MQTT (or a different protocol) for a messaging app.

The push notifications will send a signal to your app that it needs to wake up and then use MQTT to download the messages. You can also include the text message in the push notification.

However it is useful to have full control once the process is running and not rely on the system push notifications.