During acquisition, the US-based protagonist would pay no USA income taxes ($0.00) on the new valuable mass: Nickel-iron is not cash or otherwise negotiable.
If the mass of nickel-iron is located on Earth, local property taxes may apply, but that's outside the scope of the question.
If the protagonist instead received cash (or a negotiable instrument) for the full $14T, then income taxes would be due immediately. But that's also not what the question asked.
If the protagonist is not a US citizen AND is not working in the USA, then the USA IRS has no claim.
As the assets are sold, the protagonist pays USA income taxes on income from those sales. Even if those sales occur outside the USA. The IRS may use a "fair market" valuation, which may be higher than the sales price - this prevents sweetheart deals, false forced sales, and other frauds to avoid taxes.
- Since the Earth's entire iron ore market is worth only around $200 billion annually, obviously it will take decades for the protagonist to successfully liquidate without enormously disrupting the market.
If the protagonist instead donates or gifts part of the mass to somebody else, the protagonist may owe taxes on the increase in value that occurred during the time that the protagonist owned it.
- Since the mass of nickel-iron seems enough to depress the price of the commodity, and to keep it depressed for at least 10 years, it seems unlikely that the protagonist will owe any taxes from change-of-value.