Theory says black holes might be able to transport you to other places.
In principle, the mathematics of black holes shows they might be able to transport you to another region of space or possibly another universe. However, the mathematics also shows that the connection only lasts for a fraction of a second at a time, and that the link to other universes depends on a specific set of conditions, which may not even exist.
Even if it were likely, however, the strong gravity field of a black hole tears apart any material falling into the hole. So once anything, including light, crossed the so-called event horizon, it would sink into the gravity well and would not come out the other end looking anything like how it went in.