Halakhah for Bava Batra 258:9

And also that which they said (Bava Batra 129b) about this matter, that [if] one says to [someone else], "My properties are yours; and after you, for x" - if the first is eligible to inherit, the latter has nothing in place of the first. As since [the first] acquired the properties and he is eligible to inherit them, their is no further interruption of the inheritance because of the stipulation of the bequeather. And with the best commentaries, and proper logic, we learned in the chapter [entitled] Yesh Nochalin (Bava Batra 125b) that even if he says it with an expression of "from now," as for example [if] he said to him, "My properties are yours; and from now, after you for x" - nonetheless, the latter has nothing in place of the first, as the first is eligible to inherit (and there is nothing left after the inheritance). But if the first is not eligible to inherit and he said to him, "from now, after you, will be for x," the latter acquires the properties themselves, and the first one [only] receives the income all of his lifetime. And if he did not say, "from now," but rather [just], "My properties are yours; and after you, for x," the latter only receives what is left from the first (Bava Batra 137a, Mishneh Torah, Laws of Ownerless Property and Gifts 12:9). And if the first sells them, the latter never has the power to extract them from the purchaser, as they stay in the possession of the first all the days of his entire for all of his desires - whether to sell them or give them as a gift to anyone he wants. They are so fully in the possession of the first that if the giver said, "My properties are yours; and after you, for x; and after him, for y," if the second one dies in the lifetime of the first, they, may their memory be blessed, said in the Gemara (Bava Batra 129b), that the properties go back to the heirs of the first. As the [original ceder of the properties] did not leave anything over in his gift to the first, except for [the stipulation] that they would be given after [the life of the first] to the second, and from the second - and through his agency - to the third. And since the second died, and it is impossible for the third to acquire them through the agency of the second - as the giver had said - the properties remain in the hand of whom they are possessed and his heirs forever. And the same is true that we should rule in the way that we said, where he used the expression, "if" - for example [if] he said, "My properties are for x; and if he dies, they should be given to y" (see Tur, Choshen Mishpat 248:4 in the name of Rabbenu Yonah). As we are not coming to rule like this based on the expression, "after you." Rather, the reason of the thing is because we say that the first acquired the properties themselves and its income; and they are possessed in his hand, [unless] we can extract them from him with a strong proof [otherwise]. But where the giver wrote, "My properties are yours; and after you, mine or my heirs"; even though he did not mention the expression, "from now," in this retention, we should rule that if the recipient of the gift dies, the properties return to the giver or his heirs. And even if the recipient of the gift sells [them], the giver may extract them from the hand of the buyer when the recipient of the gift dies. As so did the sages say about this (Bava Batra 137b) - that anyone who retains [the rights to his properties] for himself or his heirs is always as if he stipulates, "This present will be for you to enjoy the profits [only] during all the days of your life."