Is it permissible to listen to songs and music—which experts have proven to be a treatment for stuttering and speech impediments—for three years, for a patient, and with a doctor's diagnosis?

The answer is:

Praise be to Allah.

There is no doubt that music is unlawful. The evidence for this is well-known from the Book and the Sunnah, and from the sayings of the Imams of Islam.

Allah, the Exalted, says: "And of mankind is he who purchases idle talk to mislead [others] from the way of Allah without knowledge and takes it in ridicule. Those will have a humiliating punishment." (Luqman 31:6)

The majority of exegetes have interpreted "idle talk" (lahw al-hadith) as singing and musical instruments.

Al-Bukhari reported in his Sahih (5590) that the Prophet (peace and blessings of Allah be upon him) said: "There will be people from my Ummah who will consider unlawful sexual intercourse, silk, wine, and musical instruments lawful."

If music is unlawful, then it is not permissible to use it as a cure, because it is not permissible to seek a cure through unlawful things.

Tariq ibn Suwayd (may Allah be pleased with him) asked the Prophet (peace and blessings of Allah be upon him) about making wine for medicinal purposes, and the Prophet said: "It is not a cure; rather, it is a disease." (Narrated by Muslim, 1984)

Ibn al-Qayyim (may Allah have mercy on him) said: "Seeking a cure through unlawful things is abhorrent in the Sharia and in reason. In the Sharia, because the Prophet (peace and blessings of Allah be upon him) forbade seeking a cure through unlawful things. In reason, because Allah Almighty only forbade it due to its evil nature. So, it cannot be a cure, because it is a disease in itself. If it were to remove pain from one side, it would cause greater pain from another side. Just as eating unlawful food causes disease and sickness to the heart, and the body's strength from it is only temporary and will soon transform into weakness, likewise with medicines. Indeed, their harm and sickness are greater than their benefit." (Zad al-Ma'ad, 4/146)

The Prophet (peace and blessings of Allah be upon him) said: "Allah has not placed your cure in what He has forbidden to you." (Narrated by al-Bayhaqi in al-Sunan al-Kubra, 10/5; authenticated by al-Albani in Sahih al-Jami', 2355)

The Prophet (peace and blessings of Allah be upon him) also said: "Allah created the disease and the cure, so seek a cure, but do not seek a cure with unlawful things." (Narrated by al-Tabarani; authenticated by al-Albani in Sahih al-Jami', 1761)

Even if it were proven that music is a cure for stuttering, it would still not be permissible to use it as a cure due to the unlawfulness of music.

As for the statement that two just doctors have confirmed it: This statement is not true. It is not possible for two just doctors to confirm something that contradicts the clear texts of the Quran and Sunnah. If the doctors were to confirm it, they would not be just, or their statement would be considered a mistake.

And Allah knows best.