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.
Collecting donations to pay them to the Quran teacher is considered guiding others to good deeds, and you shall earn a reward for it based on the general indication of the statement of the Prophet : "He who guides to an act of goodness will earn a reward similar to that of its doer." [Muslim and others]
He also said, "Every act of kindness is an act of charity, and whoever guides to goodness is like its doer..." [Al-Bayhaqi in Shu'ab Al-Eemaan - Al-Albaani graded it saheeh (sound)]
However, the Sadaqah Jaariyah means the Waqf (endowment). As-San‘aani said in his book Subul As-Salaam, "The scholars explained that Sadaqah Jaariyah refers to the Waqf. "
The Prophet, sallallahu ‘alayhi wa sallam, said, "When a man dies, his deeds come to an end, except for three: a continuous charity..." An-Nawawi commented on the hadeeth, saying, "The continuous charity is the Waqf."
Shaykh Ibn ‘Uthaymeen said, "All the good deeds whose effects are of a lasting nature fall into the category of the continuous charity. It is not necessary, though, that the effects last forever, because nothing lasts forever. But if something is fixed, it lasts, such as real estate, houses, and the like; these are considered continuous charity." [Fataawa Liqaa' Al-Baab Al-Maftooh]
Waqf means the detention of a specific thing and the devoting of its profit or products for charitable purposes and the like. Accordingly, the endowment is not to be sold; so it mostly lasts after the person's death, and thus his good deeds continue after his death as long as the benefits that the endowment yields continue. This does not apply to the money paid to the Quran teachers. However, every participant in this righteous deed shall be rewarded; the donors, the ones collecting the money, and the Quran teachers. They shall all be rewarded, each according to the efforts which they exerted. Indeed, Allah, the Exalted, does not let the good deeds of any person go lost. Allah, the Exalted, says (what means): {And their Lord responded to them, "Never will I allow to be lost the work of (any) worker among you, whether male or female...} [Quran 3:195] He also says (what means): {So whoever does an atom's weight of good will see it, And whoever does an atom's weight of evil will see it.} [Quran 99:7-8]
Allah knows best.