Legal clarification on property distribution and heir consent

I seek your guidance on a matter concerning the distribution of ancestral property within a family, governed by Muslim Personal Law in Uttar Pradesh.

Background:

• Mr. X passed away in 2015, leaving behind his wife, five sons, and two daughters.​

• In 2016, one of his sons, Mr. Y, also passed away, survived by his wife, Mrs. Z, and their two children.​

• In 2019, both family convened a meeting to determine Mr. Y's share of Mr. X's property.​

• It was agreed that Mrs. Z would receive Mr. Y's share in monetary terms.​

• An adjustment was made to deduct an amount Mrs. Z owed to Mr. Y's mother, as her share from Mr. Y's estate exceeded what Mrs. Z was to pay.​

• Mrs. Z agreed to this arrangement and attempted to pay balance amount via a cheque issued by her brother. However, the cheque was never deposited, and the payment was not completed.​

• A written record of this meeting, signed by multiple witnesses from both sides of the family, is available.​

Current Situation:

• Mrs. Z has severed all ties with our family for the past eight years, with no communication or contact.​

• The remaining heirs—Mr. X's wife, four sons, and two daughters—wish to proceed with the formal distribution of Mr. X's property among themselves as Mrs Z and her children have no right now in Mr X property because of settlement and adjusted of amount already done.​

Queries:

1. Is it legally permissible to proceed with the property distribution among the remaining heirs without obtaining Mrs. Z's signature, given the prior agreement and her prolonged absence?​

2. What steps should be taken to ensure that this distribution is legally sound and to prevent any future claims from Mrs. Z or her children?​

3. Would documenting the efforts to contact Mrs. Z, despite her lack of response, suffice in demonstrating due diligence?​

4. Should we consider publishing a public notice or taking any other legal measures to safeguard against potential disputes?​

Your expertise on these matters would be greatly appreciated to guide us through this process lawfully and amicably.