Is a Muslim religiously permitted to give charity to a poor person and ask that he make Du‘aa’ (i.e. supplication) for him, especially ata time of affliction?

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 ‘alayhiwasallam, is His slave and messenger.

A Muslim asking his fellow Muslim to pray for him is permissible. This also applies to a donor who asks the recipient to make Du‘aa' for him. Even the poor or recipients of charity should do so of their own accord in line with the Hadeeth in which the Prophet, sallallaahu ‘alayhi wa sallam, said: "Whoever does you a favor, then respond in kind and, if you cannot find anything to give him, then make Du‘aa' for him."[Ahmad and As-haab As-Sunan]

In a Hadeeth narrated on the authority of ‘Aa'ishah, may Allaahbe pleased with her, she said: "A ewe was sent to the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, as a gift. He said, 'Share it'. When the maidservant came back, she `Aa'ishah asked the servant, 'What did they say?' The servant replied, 'They said:‘May AllaahBless you.' To this ‘Aa'ishah said, 'And may AllaahBless them too. We respond to their Du‘aa' in kind and our reward remains.'" [An-Nasaa'i, Al-Albaani: Good Isnaad]

In addition to the great reward entailed by it, charity may also be a cause for curing illnesses by Allaah The Almighty in response to invocations by the poor. The Prophet, sallallaahu ‘alayhiwasallam, reportedly said: "Treat your patients through giving charity." [Al-Albaani: Hasan]

Allaah Knows best.