I wasn't aware that the IRS limits the number of times electronic payments can be made.  I just looked that up for my own education and see that the limit is supposed to be by form series.  This means your client might try (and I don't know whether it works) making another payment or two as 4868 extension payments since he has already maxed out the 2 times allowed for 1040 series: https://www.irs.gov/payments/frequency-limit-table-by-type-of-tax-payment

If this doesn't work, his only other option would be to pay by international wire transfer.  Here's a link with more information about how the remittance should be made.  Forget about the Same-Day Taxpayer Payment Worksheet the article asks taxpayers to bring to the bank as international banks would not understand or accept these forms, from personal experience, but just make sure your client includes all the vital information such as US TIN, taxpayer's name, tax type code, and tax year ((in addition to the IRS' account and routing numbers): https://www.irs.gov/individuals/international-taxpayers/foreign-electronic-payments

Please let us know how it goes.  Would be good to learn from your experience.