How do I prove I've made a payment to someone's account.

Just take a screenshot of the payment and send it to them.

what bank are the 2 accounts in question? Online transfers are much improved in Ireland speed wise so not sure how this could have happened especially if you’ve paid them in the past

Did they give you the right account number. Perhaps they have 2 active accounts with the 1 bank i.e. a family saver and a day to day account and the funds have gone to the account they haven't checked.

Screenshot or let them see your online banking account if you can see them in person.

Some banks don't let you screenshot but there are ways around that too.

That's an awkward situation. Did you try ringing BOI and seeing if they can help either resolve or prove it to the other party for you?

I forget the name of the number but your bank can give you basically a transaction number that they use in their back end for the recipients bank to locate it.

Years ago I worked for a company where customers frequently claimed not to get money.

We'd get them this number and not a single one didn't get their money.

Your bank will be able to fill in the blanks with my memory, it was a few years ago.

BOI should have been able to provide you a copy of the processed payment by now. If the AIB account is still active to receive money then the most likely scenario is one of BOI or AIB holding the payment for something like Fraud AML or Sanctions. Check that you did not input on your payment any funny terms vague abbreviations or other peoples names on your remittance information it's crazy the amount of random innocent looking phrases that can hold a payment up

If it were swift at least you could get the swift message to trace the funds. SEPA is seriously lacking in this traceability

Did you put anything into the message field? Often payments get stopped by investigation by banks if there is anything that could be perceived to be suspicious even if previous transfers have been made.

eg, there a number of names that appear on sanction lists that would be stopped and reviewed. People have sometimes jokingly put stupid stuff like "IRA membership" etc into these fields, these payments get stopped and manually reviewed in order to be investigated. They go into queues that could have hundreds to be investigated and can be delayed for up to 10 days due to back logs and staff shortages.

It could have just been flagged then for random investigation, this can also happen unfortunately. You won't get an alert or message stating that it has been stopped though for AML reasons, technically this could be deemed as tipping off until the payment is investigated.

The receiver will have to contact their bank to query the status of the funds.

Sometimes you just have to call into the bank and make a fuss :(