In my humble view (all below arguments should be treated as without prejudice to each other):
A. As your client have not paid subject taxes under RCM u/s 74, blockage of ITC u/s 17(5)(i) is not the issue under consideration here. I am further presuming that the supplier was not registered under GST when subject services were received by your client in FY 17-18 and that your client have raised invoice u/s 31(3)(f) (lets say, in Sept, 2023) & paid subject tax-liability under RCM immediately thereafter. I am also presuming that your client are entitled for 100% of ITC so claimed and Rule 42 & 43 are not in the picture here.
B. Time-limit u/s 16(4) of the CGST Act, 2017 does not apply to ITC availed against "an invoice issued in accordance with the provisions of clause (f) of sub-section (3) of section 31" of the recipient of goods / services.
B1. Section 16(4) deal with 'input tax credit in respect of any invoice or debit note for supply of goods or services or both' whereas invoice u/s 31(3)(f) deals with ''an invoice in respect of goods or services or both received by a registered person who is liable to pay tax under sub-section (3) or sub-section (4) of section 9 from from the supplier who is not registered on the date of receipt of goods or services or both".
B2. The words 'any invoice' used in Section 16(4) cannot be equated with 'each & every type of invoice' specially when same are followed by the words 'for supply of goods or services or both'. One cannot interpret Section 16(4) as if the words 'for supply of goods or services or both' does not exist there.
C. Delay in issuance of invoice u/s 31(3)(f) cannot be used as reason to deny ITC using restrictions u/s 16(4). Section 16(4) is concerned about 'Date of invoice / debit note' and NOT the timing of underlying supply. The words used in Section 16(4) (i.e. following the end of financial year to which such invoice or debit note pertains or furnishing of the relevant annual return, whichever is earlier) needs to be seen in this context,
C1. Above-said the intent of law is duly made clear in the Memorandum explaining the Finance Bill, 2020 states that "Clause 118 of the Bill seeks to amend sub-section (4) of section 16 of the Central Goods and Services Tax Act so as to delink the date of issuance of debit note from the date of issuance of the underlying invoice for purposes of availing input tax credit.
C2. Thus, since beginning i.e. 01.07.2017, time-restrictions u/s 16(4) in respect of any invoice was time-limit calculated from date of invoice when it was issued and NOT from "the date when such invoices was ought to be issued on account of 'time of supply provisions' read with Section 31, rule 46 & 47 & so on OR actual invoice date, whichever is earlier".
D. Availment of ITC against invoices issued u/s 31(f)(3) is always 'subject to payment of taxes' as per Rule 36(b) read with Section 16(2)(a). And as the assessee has paid these taxes only in Sept, 23 after raising invoices u/s 31(3)(f) in Sept, 23 only, he is entitled to avail ITC only in Sept, 23 or there-after. Restrictions u/s 16(4) needs to be seen in this context even though I agree with the legal proposition that this restriction u/s 16(4) is in addition to 'conditions prescribed u/s 16(2)' to avail ITC. This is because date of invoice u/s 31(3)(f), month when taxes were paid under RCM and earliest date of eligibility to avail ITC was Sept, 2023 only and NOT earlier.
In summary, I hold a view that your client are entitled to avail ITC in subject situation under discussion here read with presumptions taken in Para A above.
These are ex facie views of mine and the same should not be construed as professional advice / suggestion.
TaxTMI 
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