Is a settlement regarding a disputed property ownership valid if it involves exchanging the disputed portion for another property?

Primary text

If a claimant asserts ownership over one-third of a house, and the alleged owner denies it, but then they settle such that the claimant receives one-third of another house in lieu of their claim, the settlement is valid. Preemptive right of redemption (Shuf'ah) becomes obligatory upon the recipient concerning the portion of the other house received in settlement. This is because the claimant asserts the validity of their original claim and that what they received is compensation for the disputed third. Therefore, the consequence of their claim applies, and Shuf'ah is mandated. The denying party is not subject to Shuf'ah regarding the property given up because they maintain that the property remained their undisputed property, and they only transferred a third of their house to the claimant to satisfy their claim and avoid the harm of litigation and swearing an oath.