It would be the date the brokerage issued the payment. Absent you explaining the situation that is the best anyone can tell you.It involves death, and inheritance and who is liable for what portion of the tax burden (to put it simply, without writing a few paragraphs).
The exact dates are very important given the situation.
The date of distribution is the date the trustee took the funds out of the IRA and wired the funds to you. That would appear to be the July 2 date on the brokerage statement.The IRA distribution was made via ACH withdrawal.
I initiated it in late June, though it shows on my brokerage statement: 07/02/18 Distribution ACH WITHDRAWL $xxx
The money was received on July 3rd.
Should I go with the brokerage statement date?
Ok, but in that case the question would not be the date of distribution, as the OP asked, but the date of contribution to the new fund.If he's talking about tax accruing for the entity to which the funds were transferred (assuming it's a different entity than whomever holds the IRA).