Is it permissible to transfer the reward of good deeds, such as donating for the construction of a mosque or giving charity, to another person after performing them?

The amount you contributed to the construction of the mosque has become an endowment (waqf). It is not permissible for you to take compensation for it or dispose of it. Likewise, what your mother gave to the poor, if it was received, then he owns it by virtue of possession, and it is not permissible to revoke it or sell it; because charity becomes binding upon acquisition.