Great questions! If he is blocking the number on his phone, the message may still show up in in the message log online as the message is still being delivered to the phone but the phone itself is not displaying the message.
Alternatively, we have a Family Allowances feature that you can add to your account which allows the parent line on an account to block numbers from calling or texting lines on your account at the network end. Messages/calls blocked by Family allowances will never make it to the phone as they are being blocked before being delivered to the phone. Please keep in mind that this only blocks standard text messages or calls. In today's world, there is a plethora of other social apps that can be used for calling or texting using the phones data plan or Wi-Fi connection which do not show up on the bill at all other than a few MB of data usage.