Du`a of a Fasting Person: When?
Question

In the Hadith, it mentions “three whose supplication is not rejected,” among whom is “the fasting person when he breaks his fast.” 
Does the supplication have to be offered at the time of breaking the fast, or is it permissible to delay it until any time after breaking the fast, such as during Maghrib prayer, or until the time and place is suitable, when he can be on his own and offer supplication?
Praise be to Allah.There is a report regarding the virtue of the supplication of one who is fasting, and stating that it is answered. This report was narrated by At-Tirmidhi (2526) from Abu Hurayrah (may Allah be pleased with him), from the Prophet (blessings and peace of Allah be upon him), who said: “There are three whose supplication is not rejected: a just ruler, the fasting person when he breaks his fast , and the supplication of one who has been wronged is lifted up above the clouds, the gates of heaven are opened for it and the Lord, may He be Glorified and Exalted, says: `By My Might, I shall surely grant you support you [against the wrongdoer], even after some time.’” (Classed as authentic by Al-Albani in Sahih At-Tirmidhi)
According to a report narrated by Ahmad (8030): “… and the fasting person until he breaks his fast.” This Hadith was classed as authentic by Shu`ayb Al-Arna’ut in Tahqiq Al-Musnad.
So the supplication of the fasting person that is answered is that which he offers whilst he is fasting, until he starts to break his fast, and not after that.
Al-Munawi (may Allah have mercy on him) said: “… And the fasting person until – and according to another report when – he breaks his fast” by actually doing that, or when the time for breaking the fast begins." (Sharh Al-Jami` As-Saghir,  1/477)
Al-Qari (may Allah have mercy on him) said: “When he breaks his fast”– because breaking the fast comes after doing an act of worship, when one is in a state of beseeching and humility." (Mirqat Al-Mafatih,  4/1534)
Shaykh Ibn `Uthaymin (may Allah have mercy on him) was asked: The fasting person has a supplication that is answered when he breaks his fast. When should this supplication be offered: before breaking the fast , whilst breaking the fast or after that? Are there any supplications that were narrated from the Prophet (blessings and peace of Allah be upon him) or any supplication that you can suggest to be offered at this time?
He replied: 
“The supplication should be offered before breaking the fast at sunset, because that will combine the person’s being in a state of beseeching and humility before Allah, may He be Glorified and Exalted, with his fasting, and each of these are means of receiving a response.
As for the time after breaking the fast, the person will be in a state of rest and joy, and he may become heedless.
But there is a Dhikr that was soundly narrated from the Prophet (blessings and peace of Allah be upon him). After making the fast, he would say: “Dhahaba Al-Dhama’u wabb talat Al-`uruq wa thabata Al-ajr in sha Allah (Thirst is gone, the veins are moistened and the reward is certain if Allah wills).” This can only be said after breaking the fast .
It was also narrated that one of the Companions used to say: “Allahumma laka sumtu wa `ala rizqika aftartu (O Allah, for You I have fasted and by Your provision I have broken the fast).”
So you can call upon Allah offering the appropriate supplication that you think you need to offer." (Al-Liqa’ Ash-Shahri, 8/25)
So strive to offer supplication before you break the fast, and when you start to break the fast .
Some of the scholars said that this includes the time after breaking the fast too; in other words, after starting to break the fast.
It says in Fatawa Al-Lajnah Ad-Da’imah: Question: The Messenger of Allah (blessings and peace of Allah be upon him) said: “At the time of breaking the fast, the fasting person has a supplication that will not be rejected. What is meant by the supplication of the fasting person at the time of breaking his fast? Does it mean the supplication that the fasting person offers a few moments before breaking his fast, or is it straight after breaking the fast?
Answer: 
“This Hadith was narrated by Ibn Majah. It says in Az-Zawa’id: Its chain of narration is authentic, and the supplication may be before or after breaking the fast, because the word `Inda ( translated here as “at the time of”) includes both.
And Allah is the source of strength. May Allah send blessings and peace upon our Prophet Muhammad and his family and Companions.” (Bakr Abu Zayd, Salih Al-Fawzan, `Abdullah ibn Ghadyan, `Abd Al-`Aziz ibn `Abdullah Al ash-Shaykh." (Fatawa Al-Lajnah ad-Da’imah (9/30), Vol. 2)
And Allah knows best.