The fund herein provided for on the effective date shall supersede and take the place of and have transferred to it the assets of any county pension fund as herein defined in operation in the county, and the fund herein provided for shall be a continuation of such county pension fund.
     All annuities, pensions and other benefits allowed prior to the effective date by the board of trustees of such County Pension Fund and all claims pending or ungranted on the effective date which thereafter are allowed according to the law establishing such County Pension Fund by the board herein provided for, shall be paid by the board from the fund herein provided for, according to the law or laws under which such annuities, pensions, or other benefits were allowed.