difficult question because trying to explain it, the novice might get the wrong ideas.
Now Buddha was not an annihilationist, mundane right view for the puthujana includes, that there is the next life, there is a result of kamma or good and bad actions..., there are other worlds (heaven and hell) etc...in other words that there is dependent co arising.
Buddha never said, after death, that's it.
Now explaining nibbana is something else altogether where even greater care is required in that Atta is not explained with the confusion of other contemplatives -- it is explained in terms of experience of sati or mindfulness -- body in body, feeling in feeling, mind in mind, dhamma in dhamma.
So Atta is described in terms of what it is NOT. It is NOT the 5 aggregates subject to clinging. It is NOT the 6 senses and it's objects.
In several suttas about anicca, dukkha, anatta Buddha states clearly:
If Form were Atta, one would be able to say, "let my form be thus"
If Feeling were atta (or self), one would be able to say, "let my feeling be thus"...etc.
So here, Buddha does not deny that there is an Atta, but defines what the true self is capable of -- atta is that which is fully controllable.