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You cannot take a lump sum distribution from the annuity contract and purchase another annuity at another insurance and have it qualify as a tax-free 1035 exchange. The assets must be sent directly by the insurance company of the existing contract to the insurance company providing the new annuity contract.
To execute the 1035 exchange you would complete a 1035 exchange assignment form from the new company. The new company will complete the form agreeing to accept the exchange and forward the form to the old company. You will also probably have to sign nonqualified beneficiary acknowledge forms with the new company. The old company will then send the funds directly to the new company.
If the old insurance company issues a 1099-R they should enter code 6 in box 7 of the form which advises the IRS that it is a 1035 tax-free exchange. You would not have to report this on your tax return.
See codes on page 7 - http://www.irs.gov/pub/irs-pdf/f1099r.pdf
It should be established as a beneficiary account with the current insurance company before the exchange. See the link below for an example of the processing steps.