Short answer. Yes to both. The inheritance includes the transmissible rights your father held at death — such as his pending claim to the property — and it also includes whatever has accrued to the estate since the succession opened, so later additions to the estate belong to the heirs too.

What the law says

The inheritance of a person includes not only the property and the transmissible rights and obligations existing at the time of his death, but also those which have accrued thereto since the opening of the succession.

Civil Code, Article 781 — Property Accruing After Death. Read the full provision →

The pending claim is a transmissible right

The inheritance includes the transmissible rights and obligations existing at the time of death. Your father's pending lawsuit to claim the property represents exactly this kind of right — a legal claim that had not yet been resolved when he died, but that belonged to him and was capable of passing to his heirs. Because the statute expressly includes such rights within the inheritance, the heirs generally step into that claim rather than seeing it disappear with your father's death.

Property accruing after death is also included

The article goes further than just the property and rights existing at the moment of death — it also brings in whatever has accrued thereto since the opening of the succession. This directly answers the second part of your question: additions to the estate that arise after your father's death, but that flow from what he left behind, become part of the inheritance the heirs are entitled to, not a windfall that bypasses them.

"Transmissible" is the operative limitation

Not every right a person holds survives death — the article's protection extends specifically to rights and obligations that are transmissible. Rights that are personal to the deceased and do not survive death, by their own nature or by law, fall outside this rule even if they existed at the time of death. Whether a particular pending claim qualifies as transmissible generally turns on whether it is the kind of right that the law allows to pass to successors rather than one tied uniquely to the deceased's own person.

What this article does not itself resolve

This provision establishes that the pending claim and later accruals form part of the inheritance — it does not itself decide the merits of your father's underlying lawsuit, nor does it specify the procedural steps for the heirs to be substituted into that pending case. Those depend on the facts of the claim itself and on the applicable procedural rules governing substitution of parties when a litigant dies during a case.

Cases citing this provision

These Supreme Court decisions cite the provision above. We list them so you can read them yourself; the summaries of what each decided are not ours to give.

Related provisions

Note. Statute text quoted on this page is reproduced from the official enactment and is linked to the full provision. The explanation around it is general legal information from Vivas & Nobles Law Office, not legal advice. Whether it applies to your situation depends on facts only a lawyer reviewing them can assess.