Could we say ((may Allah reward you greatly)) to the non-believers when they do a good work?((May Allah reward you greatly))...

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

We do not find anything in religion preventing someone from praying for a non-combatant non-believer who does a favor to a Muslim by saying, "may Allaah reward you greatly," based on the general indication of the relevant Hadeeth: The Prophet, sallallaahu ‘alayhi wa sallam, said, “If kindness is done to someone and he says to the benefactor, ‘May Allaah reward you well,’ then he has reciprocated in full.” [At-Tirmithi - Al-Albaani graded it Saheeh (sound)]

The scholars have explicitly stated that it is permissible to pray for an unbeliever to be guided and to accept Islam or to pray for his worldly interests, such as his wealth or offspring, as long as he is non-combatant (not at war with Muslims). Indeed, all these things (prosperity, wealth, offspring and guidance) are entailed in praying for Allaah to reward him. For more benefit, please refer to Fatwa 89943.

In brief, in our view there is nothing preventing someone from praying to Allaah The Exalted for an unbeliever who does him a favor by saying, "May Allaah reward you greatly". One may intend by it that he be guided to Islam, and this is the greatest reciprocation one can offer an unbeliever who does one a favor.

Allaah Knows best.