If a person steals or cheats someone of money and then repents and intends to repay the same amount, how he can repay this money if he doesn't know the person or cannot contact the person? Can he pay beggar or needy person the same amount of money? If not then what he should do? To whom he should pay? Can he pay to any religious institution?

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 is His slave and Messenger.

Whoever takes a property without being his right, he should free himself by returning it to its legal owner.

Abu Hurayrah narrated that the Prophet said: “He who has done a wrong deed affecting his brother's honor or anything else, let him ask his brother's forgiveness today before the time (i.e., the Day of Resurrection) when he will have neither a dinar nor a dirham. If he has done some good deeds, a portion equal to his wrong doings will be subtracted from them; but if he has no good deeds, he will be burdened with the evil deeds of the one he had wronged in the same proportion.” [Al-Bukhari]

If one cannot return the money to its actual owners, he should spend it in charity to the needy and poor. If the legal owner of the property is found, and he has demanded it, then one has to pay him the money and he will be rewarded on whatever he had spent in charity. If one is unable to face the real owner for any reason, he should try his best to return this property to its real owner without informing him.

Allah knows best.