Is it permissible to use the money given by a mother for the purpose of helping to build a mosque for another charitable deed, such as a general charity (sadaqah) or another good work, with the intention that it is from her?

The money your mother paid for building the mosque was a trust (amanah) that you should have handed over to the competent authority. However, since you forgot the amount in your wallet, there is no sin upon you, Allah willing, because the Prophet, peace and blessings be upon him, said: "Indeed, Allah has pardoned for my Ummah their mistakes, their forgetfulness, and what they are forced to do."