All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
The general rule in Sharia is that the preemption claimant (Shafi') acquires the share at the price agreed upon in the contract between the original seller and the buyer. Al-Khatib al-Sharbini, a Shafi'i jurist, stated: "The preemption claimant takes their share from the buyer at the known price that was agreed upon in the sales contract" (Al-Iqna' fi Hall Alfaz Abi Shuja', v.2/pp.337).
As for the amounts incurred by the buyer as interest or Murabaha to purchase the share of the original seller, the preemption claimant is not obligated to bear them. This is because what the preemption claimant contributes from the price to the buyer is in exchange for what the buyer has given, while it is essential to note that taking a loan with interest is prohibited by Sharia.
Therefore, the preemption claimant is not obliged to pay the interest incurred by the buyer for the purchase of the shared portion. And Allah The Almighty Knows Best.