Dear Sh.Agarwal Ji,
As already explained above, Rule 34 (2) talks of "the date of time of supply of services" in terms of Section 13 of the Act and Section 13 (2)(a),(b) & (c) explains as under:-
(a) the date of issue of invoice, if issued within prescribed period;
(b) the date of provision of service, if invoice is not issued within prescribed period;
(c) the date of receipt of service in books of accounts where (a) and (b) do not apply.
Rule 34 emphasizes on "date of supply" of service. Supposing that invoice has not been issued within prescribed period we are to resort to Section 13(2)(b). What (b) emphasizes that is the date of provision of service. "provision' does not always stand for 'clause' . Here provision means to provide service i.e. the date of providing service. It is relevant to mention that there is no no difference between "Supply of service " and "Providing of Service". You are talking of completion of service and I am emphasizing on "Supply". Service can be supplied/provided in piecemeal also in case of continuous supply of service e.g. Construction Service. This situation is not applicable to your case because " intermediary services" do not conform to the term,"Continuous supply" . The date of provision of service does not mean the date of completion of service. The word, "Completion" is neither present in Section nor in Rule. . In the absence of date of invoice, one is to resort to the date of providing/supplying service or receipt of payment, whichever is earlier. Receipt of payment is last resort. The phrase "date of receipt of payment" stands for the date of receipt of consideration on account of services supplied/provided.
What type of evidence you have for the date of providing service/supplying service in the absence of 13(2)(a) i.e. the date of invoice. So the date of supply is the determinant factor whether in the form of date of invoice or in some other form i.e. Contract, books of account. You are to stick to the date of supply of service. If you cannot ascertain as per (a), go to (b); if you cannot ascertain as per (b), go to (c).
If I agree with you that the date of completion of service is the date of provision, what documentary evidence you have to prove ?
The date of supply is relevant for determination of rate of exchange. You are to see whether you fall under Section 13(2)(a) or (b). If not ascertainable in both, then (c) will be determinant factor.