From the perspective inside a black hole: Is information about everything outside a black hole - the rest of the cosmos - represented on the inside of the (event) horizon too? NB. I realize it is the notion of a so called stretched horizon that is being used about the 2d-like sheet that information is scrambled on, but I haven't heard about its view-from-the-inside-analogy, that naively being a horizon hovering just "below" the event horizon; therefore the simplified use of "event horizon" in the question. I also realize that it would be impossible to sample (all) this information as an inside job, which I would suppose could have some bearing on the answer to the question.
Answer
I cant speak in the case of full generality, but at least for Schwarzschild and Reissner-Nordstrom (electrically charged) non-rotating black holes, there exists a coordinate system called 'isotropic coordinates'; it turns out that in these coordinate systems the 'interior' and 'exterior' regions are actually isomorphic; this means that representing the solution in these coordinates gives rise to two identical yet causally disconnected regions of space-time. These two space-times share a common boundary, namely the event horizon.
As such, the two regions can be thought of representing the same physics and the answer to your question is then a definite 'yes': the information contained within the 'interior' section also amasses on the horizon.
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