Can I ask/incentivise inherited tenants to sign my lease?

[Cat L.]

We just purchased a property with existing tenants and a 12 mo lease in Texas (Tarrant county). They are brand new so we have no idea of their quality (and the previous landlord didn't even get a security deposit!).

We don't want to change their rent/basic terms, but we'd like them to sign our lease as theirs is a bare bones affair that doesn't address a number of fine points we like to have covered.

As I understand it, we can't make them change terms, which is fair. But could we offer to take $100 off next month's rent if they agree to switch to our lease? I assume there's no legal impediment to the willing transfer of terms from one lease to another, but I can't find this exact situation addressed.

Thanks for any help!