Kindly refer to the section 31(3)(f), reproduced below:
"(f) a registered person who is liable to pay tax under sub-section (3) or sub-section (4) of section 9 shall issue an invoice in respect of goods or services or both received by him from the supplier who is not registered on the date of receipt of goods or services or both;"
Therefore, legitimate liability to issue self-invoice is on the date of receipt of services. Hence, a registered person cannot take the shelter of delay made in issuance of self invoice for the claiming eligibility of input tax credit considering the transaction to be of a financial year in which self-invoice has been issued instead of FY to which it pertains.
Further, the capping of section 16(4) specifically mentions "financial year to which invoice.....pertains". This essentially clarifies the intention of law makers.
Hence, it should be considered as transaction pertaining to FY 2018-19.