I don't believe the fact that the client passed away changes the nature of the income.  Sounds like there is nothing to report on the 1041.

When the money is given to the estate, is it being reported to the IRS in a 1099 or other?

If you, then how to prove it is not taxable if you are reporting it?

Taxpayers don't have to prove anything when filing returns, but sometimes it's a good idea to anticipate questions from IRS.  I doubt that a 1099 was issued here, and the first step would be to ask the payer why they did that.  You could attach a statement to the return explaining why it was not taxable -- not that anyone would read it, but it would remind anyone a year later of what happened, if IRS asks.  

I've asked the client whether a 1099 will be issued. Haven't heard back yet. To answer your question, I would (in that case) report it as income on page 1 and then take a deduction as well to zero it out.