[The Ruling on a Child Picking Up Lost Property]

Answer – and Allah is the One who grants success: If a child picks up lost property, then what is required of his guardian is to take it from him. It then becomes, at that point, lost property in the hand of the guardian, to which the rulings of lost property are applied. If the lost property is destroyed while in the hand of the child, or is lost from his hand, its liability is upon the child, from his own wealth.
Thus, they only said that it is obligatory for the guardian to take it from the hand of the child in order to safeguard the child’s wealth, for if it is destroyed while in the child’s hand, the liability is upon the child from his wealth.
Yes, what we have mentioned is the madhhab, as in the marginal notes on al-Sharḥ . They have considered lost property to be usurped property (ghaṣb) in the hand of the child, and for that reason they ruled that the child is liable, but they did not mention the underlying reason.
Perhaps the underlying reason – and Allah knows best – is that the child’s picking up the lost property is an aggression (jināyah) against the wealth of another, and the aggressions of children are liable from their wealth even though they are not legally accountable (mukallaf). This may be indicated by the generality of His saying the Exalted: “So whoever has assaulted you, then assault him in the same way that he has assaulted you.” [al-Baqarah:194]
Furthermore, they have held the owner of an animal liable when it destroys the crop of another, even though the animal is not legally accountable; so the aggression of a child is even more deserving of liability. There is no basis for making the guardian liable, because he is not the owner of the child. The child is the owner of himself, so the liability is upon him, from his wealth, and not from the guardian’s wealth.
What we have mentioned may also be indicated by His saying the Exalted: “And remember David and Solomon, when they gave judgment concerning the field when the sheep of the people overran it at night, and We were Witness to their judgment. So We guided Solomon to the right understanding of the case; and to each [of them] We gave judgment and knowledge.” [al-Anbiyāʾ:78–79]– and this is along with recourse to the reason for revelation.

Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.2