A few suggestions - you, as a parent, have the responsibility for what happens on his phone.  If you want to see what he is texting, and he is erasing the texts before you can see, then take the phone away.  Or block texting.  Your accessibility to the texts should be a condition of the privilege of having the phone.

What model phone is it?  If it's an iPhone or smartphone, there are apps you can install to have texts forwarded - though he can get around those if he's determined. 

You need to set rules and boundaries for him and the phone, since you are paying the bill.  If he is unwilling to abide by those rules, then he does not have the phone, or at least has limited options with the phone.