I am speaking about a case where the father said that he wanted to write a will but did not manage to, and he revealed that he wanted to give to the daughters as well.
So the son is presumed in possession, since he stands in his father's place, but since under state law the inheritance is divided equally, the daughter can delay signing away her share, and it turns out that the son will receive only a relative portion, while the daughter claims that she is fulfilling the will of the deceased, and therefore is not obligated under the law of returning lost property.
It seems to me there is some Rabbi Akiva Eiger in responsa, part 1, no. 68, who says that there is an obligation to honor the father using the father's money. The question is whether an inheritance is considered the father's money, or whether because the son stands in his place it is considered the son's money?

This has already come up here in the past. If one adopts the view (accepted by most halakhic decisors) that state law has no standing with regard to inheritances, and the law of the Torah is what determines matters (because this is a prohibition and not a monetary issue), then the money legally belongs to the son, and the daughter is obligated to sign so as not to steal it. If one holds that state law does have standing even with regard to inheritance, then the situation is of course different.
Assuming the money belongs to the son, the question arises of the commandment to fulfill the words of the deceased. See a general overview here:
https://he.wikipedia.org/wiki/%D7%9E%D7%A6%D7%95%D7%95%D7%94_%D7%9C%D7%A7%D7%99%D7%99%D7%9D_%D7%93%D7%91%D7%A8%D7%99_%D7%94%D7%9E%D7%AA

And here too you will see a discussion of whether this is a personal obligation or a property acquisition in the assets:
http://www.daat.ac.il/mishpat-ivri/skirot/151-2.htm