Assalaamu alaykum. There are many ignorant people who, whenever I ask them, “How are you?” reply, “I am well, by the blessings of your supplication,” though I have not supplicated for them. They do not say, “I am well by the mercy of Allaah.” Is this type of saying permitted?

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger. 

There is no doubt that the best reply which the Muslim should give when asked about his conditions is to praise Allah by saying, for instance, “Alhamdulillah” (praise be to Allah) or any statement to this effect. Verily, those who praise Allah often shall be the best of people on the Day of Judgment. The Prophet, sallallahu ‘alayhi wa sallam, said, “The best among the servants of Allah, the Exalted, on the Day of Judgment shall be those who praise Allah often.” [At-Tabaraani; Al-Albaani classified it as Saheeh (sound) in Saheeh Al-Jaami’ As-Sagheer wa Ziyaadatuh]

As for saying, ‘I am well, by the blessings of your supplication,’ we could not find any basis for this wording. However, if the person is saying this in reply to someone who has been supplicating Allah in his favor or in favor of all Muslims in general, then there is no harm in telling him that his supplication has been answered and its blessings are felt. There is no doubt that supplication is a means to bring about benefit, ward off harm, and receive the blessings of Allah.

Irshaad As-Saari reads, “The Prophet, sallallahu ‘alayhi wa sallam, said, ‘Satan touches every son of Adam on the day when his mother gives birth to him with the exception of Maryam (Mary) and her son. They were protected by the blessing of the supplication of Hannah (Anne), Maryam's mother.” Ibn Katheer wrote, “The grace of Allah bestowed upon the parents by the blessing of their children's supplications for them: supplication for the parent begets blessings.” [An-Nihaayah fi Al-Fitan wal-Malaahim]

It is prescribed for the Muslim to supplicate Allah in favor of his fellow Muslims; Allah, the Exalted, says (what means): {And (there is a share for) those who came after them, saying: Our Lord, forgive us and our brothers who preceded us in faith...} [Quran 59:10] The Prophet, sallallahu ‘alayhi wa sallam, said, “Whenever a Muslim supplicates for his (Muslim) brother in his absence, the angels say: ‘Amen, and may the same be for you too.’” [Muslim]

But if he says this statement to someone who has not supplicated Allah in his favor or in favor of the Muslims in general, it is meaningless and impermissible because it involves lying and does not conform to the reality.

It should be noted that saying that the supplication of a specific person begets blessing is allowed if that person is pious. Ibn ‘Uthaymeen said, “It is allowed to ascribe blessing to a person if he is worthy of that; Usayd ibn Hudhayr said when the verse on Tayammum (dry ablution) was revealed because of the lost necklace of ‘Aa’ishah, ‘This is not the first blessing from you, O family of Abu Bakr.’”

As for Tawassul, which means asking Allah by the blessing of someone and supplicating Allah by means of it, it is a religious innovation. This was verified by Shaykhul-Islam Ibn Taymiyyah who underlined that it is prescribed to make Tawassul through the names and attributes of Allah, one's good deeds, or the supplications of the living pious person.

Allah knows best.