[wyager]

It may not be possible to meaningfully answer this question in this case.

If we're talking about something like fluorescence, there's a fairy clear point where one photon disappears and another appears.

In a linear process like this, photons are not really absorbed by the material. In fact, the quantum behavior of photons is not relevant to the process, so you can just treat it purely as a wave phenomenon.

In cases like this, I would generally say that it is the "same" photon, but again, not really appropriate to think in terms of photons when there is nothing about the process that depends on quantization.