Section 12B. If a member in service, as described in subparagraph (i) of paragraph (a) of subdivision (1) of section three, including such a member in the uniformed division of the state police, who has not nominated a beneficiary under Option (d) of subdivision (2) of section twelve other than the spouse of such member and who has two full years of creditable service, dies and leaves a spouse to whom such member had been married for at least one year and with whom such member was living at the time of the death of such member, or who the board finds had been living apart from said member for justifiable cause other than desertion or moral turpitude on the part of such spouse who is eligible to receive a member-survivor allowance under the provisions of said Option (d), and so elects, and if there are any surviving children of said deceased member who are under age eighteen or over said age and physically or mentally incapacitated from earning on the date of death of the member, or under age twenty-two if a full-time student, there shall be paid to such spouse for the benefit of all such children an additional allowance of one hundred and twenty dollars a month for one child plus an allowance of ninety dollars a month for each additional child subject to the provisions of paragraph (e) of section one hundred and two.

If there is no surviving spouse of such member or such surviving spouse dies, such amount of the member-survivor allowance as would have been payable or would be payable to a spouse under the provisions of Option (d) of subdivision (2) of section twelve shall be paid for the benefit of such surviving children to a legally appointed guardian, together with the allowances provided in this section for children.

If a spouse remarries, the allowances payable for the benefit of any children under this section shall terminate and thereafter there shall be paid to a legally appointed guardian for the benefit of each eligible surviving child an allowance of one hundred and twenty dollars a month for one child plus an allowance of ninety dollars a month for each additional child subject to the provisions of paragraph (e) of section one hundred and two.

Allowances payable under this section for the benefit of a child shall terminate upon his adoption, upon reaching the age of eighteen unless he is physically or mentally incapacitated from earning on the date of death of the member, or if a full-time student upon reaching the age of 22, or on the date a child ceases to be a full-time student, or upon his marriage, whichever first occurs, or upon his death. The word ''child'' shall include a legally adopted child of the deceased member. The words ''full-time student'' shall mean a child who is in full-time attendance in an accredited educational institution offering full-time courses of study equivalent to or higher than secondary school study. The words ''accredited educational institution'' shall mean any school, college or university that is licensed, approved or accredited, as the case may be, in the state in which it is located.

If allowances are granted only under this section, any accumulated regular deductions of such member and the amount equal to the value of the regular deductions credited to his account in the special fund for military service credit, if any, together with regular interest thereon to the date of his death, shall be transferred to the pension fund, to be merged, and to be used, on a basis that shall be determined by the actuary, for the exclusive purpose of defraying the payment of such allowances, and shall not be included in the factors that enter into the ordinary determination of the pension appropriation required by paragraph (d) of subdivision (3) of section twenty-two.

If allowances are granted only under this section any amount of accumulated additional deductions to the credit of such member shall be paid in accordance with paragraph (c) of subdivision (2) of section eleven.

If allowances are granted only under this section the total annual allowance derived from and payable under the provisions of this section shall at no time be greater than the annual rate of regular compensation payable to such member on the date of his death.