; and for training, employment and case management services, allowances for job search and relocation, and related State administrative expenses under part II of subchapter B of chapter 2 of title II of the Trade Act of 1974, and including benefit payments, allowances, training, employment and case management services, and related State administration provided pursuant to section 231(a) of the Trade Adjustment Assistance Extension Act of 2011 and section 405(a) of the Trade Preferences Extension Act of 2015, $790,000,000 together with such amounts as may be necessary to be charged to the subsequent appropriation for payments for any period subsequent to September 15, 2018: Provided , That notwithstanding section 502 of this Act, any part of the appropriation provided under this heading may remain available for obligation beyond the current fiscal year pursuant to the authorities of section 245(c) of the Trade Act of 1974 ( 19 U.S.C. 2317(c) ). State unemployment insurance and employment service operations For authorized administrative expenses, $70,000,000, together with not to exceed $2,760,903,000 which may be expended from the Employment Security Administration Account in the Unemployment Trust Fund ( the Trust Fund ), of which: (1) $2,665,775,000 from the Trust Fund is for grants to States for the administration of State unemployment insurance laws as authorized under title III of the Social Security Act (including not less than $160,000,000 to conduct in-person reemployment and eligibility assessments and unemployment insurance improper payment reviews, and to provide reemployment services and referrals to training as appropriate, for claimants of unemployment insurance for ex-service members under 5 U.S.C. 8521 et. seq. and for claimants of regular unemployment compensation, including those who are profiled as most likely to exhaust their benefits in each State, and $6,000,000 for continued support of the Unemployment Insurance Integrity Center of Excellence), the administration of unemployment insurance