Disable iMessages on 1 screen time device of 2

Child has a single Screen Time enabled account across an iPhone & iPad. Downtime is set to always on with messages, phone & mail in the allowed apps, so that he can contact us and friends on his iPhone (the phone is to be used as a phone only).

As the iPhone has no data allowance on the parentshield network, the iMessages are being received on the iPad and not the iPhone when he is not at home on the wifi.

Is there a way of disabling iMessages/Messages on the iPad but not the iPhone on the same account?