You will not have to send any proof in, but keep any records that you have.
In TurboTax, enter your 1099-R just as it is issued.
TurboTax will then ask a series of questions so the program can determine if the amount is taxable or not.
At the What Did You Do with The Money screen indicate that I moved the money to an IRA or another retirement account and then select rolled over down below.
There should be no effect on your taxes.