What is the ruling on the percentage the principal requested from the inheritance in exchange for his effort in recovering it, and is it permissible to retract the agreement on this percentage?

It is permissible to appoint one of the heirs or a stranger to collect properties or compensations for a fee or a percentage. This falls under the category of lawful Ju'alah (a contract of reward/commission).

Ju'alah is a permissible contract (non-binding) that can be revoked. - If the Ja'il (the one offering the reward) revokes it before the 'Amil (the one performing the work) begins the work, the revocation is valid, and the Ju'alah is dissolved. - If the Ja'il revokes it after the 'Amil has begun the work, the 'Amil is entitled to compensation for the work he has done, or a percentage of his Ju'alah proportionate to the work performed.

Sheikh Ibn 'Uthaymeen said: "Either party can revoke it. If the 'Amil revokes it, he is not entitled to anything. If the Ja'il revokes it after the work has begun, the 'Amil is entitled to compensation for his work." The compensation is calculated as a percentage of the agreed-upon Ju'alah, not based on fair market value (ajrat al-mithl). So, if the 'Amil performs half of the agreed-upon work, he is entitled to half of the Ju'al (reward). If there are several Ja'ils and they agree with several 'Amils to collect properties for a percentage, then one of the Ja'ils revokes the agreement after the 'Amils have begun the work, that Ja'il must pay them a percentage of the Ju'al proportionate to the work they have performed, calculated from his own share in the Ju'alah.