All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Waqf (Endowment) is an act of obedience that brings a servant closer to their Lord. Umar bin Khattab got some land in Khaibar and he went to the Prophet (PBUH) to consult him about it saying, "O Allah's Messenger (PBUH) I got some land in Khaibar better than which I have never had, what do you suggest that I do with it?" The Prophet (PBUH) said, "If you like you can give the land as endowment and give its fruits in charity." So `Umar gave it in charity as an endowment on the condition that it would not be sold nor given to anybody as a present and not to be inherited, but its yield would be given in charity to the poor people" {Transmitted by Bukhari & Muslim}.
The condition set by the donor (Waqif), with regard to the endowment itself, is taken into consideration and does not contradict its purpose. For example, this condition should be observed when dividing the yield of the endowment among the beneficiaries, considering factors such as their shares, timing, prioritization, and other relevant conditions.
Imam Nawawi, may Allah have mercy on him, says: "The condition set by the donor should be observed in terms of allocation, the qualifications of the beneficiaries, and the timing of entitlement. For instance, if the Waqif designated the endowment for his poor sons or widowed daughters and included a condition of equal division between male and female beneficiaries or preferred one over the other, then his condition is followed... Similarly, if he stated it's for the benefit of the poor sons or the widowed daughters, and someone among them becomes self-sufficient or marries, they no longer fulfill the entitlement. However, if they return to poverty or their marriage ends, they regain their entitlement... Likewise, if he said, 'In the event of the death of my children, their share should go to their offspring,' his condition is followed." [Rawdat al-Talibin Vol.5, Page:335 - 338].
As for a condition, set by the Waqif, that contradicts the essence of the endowment, it is not taken into consideration or observed. Imam al-Khatib al-Sharbini, may Allah have mercy on him, stated: "The general rule is that the conditions of the Waqif are to be observed as long as they do not conflict with the essence of the endowment." [Mughni al-Muhtaj, Vol.3, Page.540].
Shaykh al-Islam Zakariya al-Ansari, may Allah have mercy on him, the Shafi'i scholar, stated: "The conditions of the Waqif are observed in what has been stipulated regarding equal distribution, preference, and specification in terms of description, time, and place." [Asna al-Matalib fi Sharh Rawd al-Talib, Vol. 2, Page. 468].
As for a condition of the Waqif that goes beyond the scope of the endowment's intent, it is not binding and does not need to be observed. However, if someone chooses to adhere to it, there is no harm in doing so.
In conclusion, the condition mentioned in the question is not binding for the Khateeb (The person who delivers the Friday sermon), because although it does not contradict the essence of the endowment (Waqf), it goes beyond its description and intent. Thus, it is not obligatory to adhere to it. However, if the Khateeb were to make a supplication for the Waqif or their family without being explicitly stipulated, there is no harm in doing so. And Allah the Almighty knows best.