The depreciation applies to the whole property, not the father's "third". What state did the two parents live in? (Is it a community property state?) What about depreciation from 2016? If simplified method was used from 2017, there is no depreciation for those years to account for.
[Edited to correct:]
At the time of the sale, the son owned 1/3 from 1999, and 1/3 from the quit claim deed. Even though there was an implied life estate, it ended when the father died and the son became the owner in full. So the son owns 2/3 the home and pays 2/3 the capital gains tax.
It appears that the son is a 2/3 owner and did not live in the home? What were the circumstances of the quit claim deed in 2011? If the idea was for the father to give his son his interest in the house to avoid probate, or to otherwise pre-dispose of assets, but the father would have the right to live there until he died, then the son may have an implied life estate, even if the deed was not a written life estate. If there was an implied life estate, and the son can't sell until his father died, then the son didn't really "own" anything (because ownership implies the right to dispose of the property as he sees fit), and that would allow you to treat the entire selling proceeds as reported on the wife/mother's tax return. So you can ignore the son's basis. The wife's basis is determined by whether you live in a community property state.
If no, then her basis is half the cost in 1999, plus half the cost of improvements, plus half the fair market value on the day her husband died (stepped up basis), minus accumulated depreciation, no matter whose tax return it was reported on. The accumulated depreciation is taxed (recaptured) but any remaining gain is covered by the full $500,000 exclusion for married couples, as long as she sells within 2 years of the date of her spouse's death.
If yes, this is in a community property state, the wife receives a full stepped up basis equal to the fair market value on the date her spouse died, and the depreciation is wiped away. Her only capital gain would be any gain in value from 2023 to 2024.
