I thought that it was about 2:240 abrogating 2:234, but it was about the other way around. That is what caught my eye first: that a latter verse is abrogated by a former one!
Dr. Mustafa Zayd, who refutes this claim in his book النسخ في القرآن الكريم, volume 2, pages 267-272 (items 1155-1165), and lists it in the last chapter of his book, entitled, "Cases famous that they were abrogated but they are not
", writes the opinion of Mujaahid that 2:240 abrogated the practice that a widow had to stay in her late husband's house for a year. He said that the mandate became four months and ten days, and the rest of the year is optional and up to her
`Ataa' agrees but says that inheritance verses (4:12) abrogated the residence requirement; a widow may mourn anywhere she wants but she is not entitled to residence support.
Dr. Zayd correctly sees the two verses like you do, Pragmatic, namely that 2:234 specifies a duty
on the widow, while 2:240 specifies a right
for the widow. Two different concerns and therefore neither one can abrogate the other.
Dr. Zayd propounded the various opinions of the scholars about these two verses, as explained by At-Tabari. At-Tabari leaned toward Qataada's opinion, i.e., only residence was abrogated by inheritance. He cites for evidence a hadeeth narrated by Furay`a, sister of Abu-Sa`eed Al-Khudri, in which she asked the Prophet (PBUH) to let her leave the house of her late husband and go to her parents house before the end of the mourning period of four months and ten days and he did not allow her. Bear in mind that she was alone in the house!
Dr. Zayd correctly concludes that the hadeeth does not address residence at all, it addresses the mandatory mourning period, thus it cannot be used for evidence that the residence allowance is abrogated. Was that really hard to conclude? The hadeeth confirms 2:234 and neither it nor 2:240 speak about residence.
Dr. Zayd does not refute the claim that 4:12 abrogated 2:240. He may have thought it was too trivial a claim and left it out. Verse 4:12 indeed has no prohibition against residence. It simply specifies the share of a widow in her husband's estate when it is divided between heirs. In other words, 4:12, 2:234 and 2:240 can all be enforced together
without conflict, so there is no cause to claim any of them abrogating any other.