I don't know about Oklahoma, but in Texas generally not, as this is something that needs to be recorded in the internal records of the partnership. However, if for some reason there was previously recorded in the deed records something like a partnership resolution appointing the prior manager as having authority to act, you might need to record something new on the deed records showing this has changed.
Generally partnership agreements are not recorded in the deed records. It used to be pretty common to record trust agreements in the deed records to show who had authority and what their authority was. Plus, trust property is technically owned by the trustee, not the trust itself. This is much less common now.
You might need to do a partnership resolution or whatever other internal document that the operator requires to show you were elected as the new manager, and send that with your notice to the operators. Your partnership amendment, if it is signed by all the partners, will probably suffice.