"Benefit year" with respect to an individual means the one-year period beginning with the first day of the first week of unemployment with respect to which the individual first files a claim in accordance with section 23-772 and thereafter the one-year period beginning with the first day of the first week of unemployment with respect to which the individual next files a claim after the termination of his last preceding benefit year, provided that at the time of filing the claim the individual has been paid the wages for insured work required under section 23-771. For the purposes of this section a week with respect to which an individual files a valid claim establishing a benefit year shall be deemed to be in that benefit year which includes the greater part of such week.