The original company's refusal to change the code to code 6 code indicates that they believe that they did not do a 1035 exchange. Whether or not the original company would permit a 1035 exchange by a beneficiary is determined by the terms of the annuity agreement.
If this truly qualified as a 1035 exchange as permitted under the terms of the annuity agreement, your only recourse would be to submit a substitute Form 1099-R (Form 4852) claiming code 6 and a $0 taxable amount. Whether or not the IRS would accept the explanation is unknown. If the funds were paid to you as intermediary rather than directly to the new annuity for your benefit, it certainly does not qualify as a 1035 exchange.
