Praise be to Allah.
Firstly:
Whoever breaks their fast in Ramadan due to a valid reason, such as menstruation or an illness that is expected to be cured, must make up for the days they missed before the next Ramadan enters.
If they delay making up the fasts until the next Ramadan arrives, many Jurists hold the view that in addition to making up the fasts, they must also feed a poor person for each day missed. Others opine that feeding the poor is recommended, not mandatory, and that the obligatory act is only to make up the fasts. Please refer to question no: (26865 ).
Secondly:
It is permissible for one who wishes to feed a poor person to give them money and authorize them to buy food with it, and once the food is purchased, to take possession of it.
The Jurists have mentioned the reverse of this scenario and have ruled its permissibility, which is that the poor person authorizes the wealthy to take possession of the Zakat money on their behalf, and by doing so, the Zakat reaches the poor person and remains with the wealthy as a trust.
The scholar Ibn Qasim (may Allah have mercy on him) said in "Hashiyat Ar-Rawd" (3/293): "If the poor person authorizes the owner of the wealth to take possession on their behalf, and to buy with it thereafter a garment or the like, it is valid." End quote from.
Please refer to the answer to question no: (339075 ).
Therefore, what you have done is permissible, which is authorizing the poor person to buy food with this money and take possession of it.
And Allah knows best.
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