Is it permissible, in Islamic law, to give money to a son who neglects his prayers out of laziness, for the purpose of improving his commercial shop, knowing that he is trustworthy and active, and the shop is incurring losses?

There is no harm in giving money to a son who does not pray, to help him, as long as it is thought that this will benefit him and not be wasted. This assistance should be a means of advising him and inviting him to return to God through prayer, reminding him that abandoning prayer is a great danger, that it is the pillar of religion, and that there is no share in Islam for one who neglects it, as the Prophet, peace and blessings be upon him, said: "Indeed, between a man and polytheism and disbelief is the abandonment of prayer." And abandoning prayer may be a reason for him to be deprived of provision, as the Prophet, peace and blessings be upon him, said: "Indeed, a man is deprived of provision because of a sin he commits." It is recommended to supplicate frequently for his guidance.