If a member of the fire department shall die before or after retirement by reason of an injury received in, or illness caused by the performance of his duty, a death allowance, in lieu of any allowance payable under any other section of the Charter or by ordinance, on account of death resulting from injury received in or illness caused by the performance of duty, shall be paid, beginning on the date next following the date of death, to his surviving wife throughout her life or until her remarriage. If the member, at the time of death, was qualified for service retirement, but had not retired, the allowance payable shall be equal to the retirement allowance which the member would have received if he had been retired for service on the day of death, but such allowance shall not be less than 55 percent of the final compensation earnable by said member immediately preceding death. If death occurs prior to qualification for service retirement, the allowance payable shall be equal to the final compensation of said member at the date of death, until the date upon which said member would have qualified for service retirement, had he lived and rendered service without interruption in the rank held by him at death, and after said date the allowance payable shall be equal to the retirement allowance said member would have received if retired for service on said date, based on the final compensation he would have received immediately prior to said date, had he lived and rendered service as assumed, but such allowance shall not be less than 55 percent of such monthly final compensation. If he had retired prior to death, for service or for disability resulting from injury received in, or illness caused by the performance of duty, the allowance payable shall be equal to the retirement allowance of the member, except that if he was a member under Section 8.585 and retirement was for such disability, and if death occurred prior to qualification for the service retirement allowance, the allowance continued shall be reduced upon the date at which said member would have qualified for service retirement, in the same manner as it would have been reduced had the member not died. If there be no surviving wife entitled to an allowance hereunder, or if she dies or remarries before every child of such deceased member attains the age of 18 years, then the allowance which the surviving wife would have received had she lived and not remarried shall be paid to his child or children under said age, collectively, to continue until every such child dies or attains said age, provided that no child shall receive any allowance after marrying or attaining the age of 18 years. Should said member leave no surviving wife and no children under the age of 18 years, but leave a parent or parents dependent upon him for support, the parents so dependent shall collectively receive a monthly allowance equal to that which a surviving widow otherwise would have received, during such dependency. No allowance, however, shall be paid under this section to a surviving wife following the death of a member unless she was married to the member prior to the date of the injury or onset of the illness which results in death.