My relative filed for income tax extension, because he had not paid/settled the tax issue back in the foreign country by the deadline to file tax here. He wanted to pay the tax in the foreign country (India) first so that he can use tax credit here/ However, his taxes in India are still not done, and extension deadline is soon approaching. Now what can be done to make sure he does get credit for the foreign tax paid?

He could file a return without the credit and then amend later to include it and get the additional refund.
Amended returns take a lot of time to be processed (a few months, especially with a refund).
He could also wait and file the return late. If he doesn't owe any taxes, there will be no penalty for filing late.