(b) Any provision of this Code to the contrary notwithstanding, where all tenants named in a lease have permanently vacated a housing accommodation, and a primary-resident family member of such tenant or tenants (first successor) is entitled to and executes a renewal lease for the housing accommodation, as provided in section 2523.5 of this Title, and thereafter permanently vacates the housing accommodation, if such housing accommodation continues to be subject to the RSL and this Code after such first successor vacates, and a primary-resident family member (second successor) is entitled to and executes a renewal lease for the housing accommodation as provided in section 2523.5 of this Title, the legal regulated rent shall be increased by a sum equal to the allowance then in effect for vacancy leases, including the amount allowed by subdivision (a) of this section. Such increase shall be in addition to any other increases provided for in the RSL and this Code, including adjustments pursuant to section 2522.4(a) of this Part, and any applicable vacancy allowance authorized by the rent guidelines board, and shall be applicable in like manner to the renewal lease of each second subsequent succeeding family member.