I think he will just phase through it.
The Science Fiction entity ^conjectured by this thread creator typically has awesome powers, and as seen in fictional works such as a particular Original Series Star Trek episode (title escapes my memory), 'plays god' while at the same time being so morally unresponsible and immature as to be a danger to all around him.
Jake would not only be immune to Natural Law in the material universe, but he would also have the power to manipulate material objects at will. Therefore, to avoid impossible eventualities such as portrayed in the mystery Star Trek episode, he would need mature and responsible 'adult' overseers, parental figures endowed with the necessary morals to prevent them from destroying the entire Universe (or that part of the Universe within their domain).
If OTOH Jake had no need of such parental oversights, then he must already possess perfectly sterling character traits and morals so as to prevent him from becoming like the cosmic brat in the aforementioned Star Trek episode.
We arrive at a reasonably durable self-evident 'truism'; 'To be capable of destroying the Universe by mental powers, you have to be so perfect and free of evil notions as to not desire to do so in the first place'. My 'proof' is that the Universe as we know it does not currently seem in any danger of being destroyed by any such entity. Like the joke about the man who sits on a park bench and tears up each page of his newspaper after reading it and scatters the pieces all around on the grass, 'to keep the elephants away' (we see no elephants, ergo; the trick works), in similar mental gyrations, the Universe and us in it still exists, therefore the notion of such irresponsible entities as the Star Trek enfant terrible being on the loose and bent on universal destruction is not to be feared.
In more direct answer to the thread's question, the super-being would pass through such material objects as black holes with impunity, and would have no desire to meddle with it.
I seem to visualize this as a sort of 'Catch-22'; to be capable of such super powers, is to be morally beyond the desire to wreak havoc in the Universe (i.e. 'Why bother?' and 'What is the point?'); whereas to have the will and the desire to do so, becomes a self-defeating Law of Nature preventing anyone willing to destroy Nature from becoming capable of doing so.
To be capable of such power and immunity in the first place, Jake would have to have a moral character so incorrupt that he would not wish to do so, viewing the very idea as virtually unthinkable.
This is all just off the top of my head. I have such a one-track mind that I don't seem oft capable of 'thinking' and 'admiring' at the same time; it's either 'the one or the other'.