It is an interesting calculation, I haven't checked the steps and Please use Arxiv links when available

First thing to notice is the Infalling shell is treated in Classical GR, and Scalar field theory is quantized in this Gravitational Background. So it is not a full calculation Involving quantum gravity.

So this wont constitute as a resolution to Black hole information Paradox. Ideally even the infalling matter must be treated Quantum Mechanically.

Assuming the calculation is correct, Trace(Pho^2) = 1 Implying that the Scalar field evolved in a unitary manner is an interesting one. But I don't know what would happen if one were to change the co-ordinate system.

I have Little expertise on this subject so many thing I would have said might be naive, Any comment/corrections will be appreciated.